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L_0718 | radioactive decay | T_3537 | There are three types of radioactive decay: alpha, beta, and gamma decay. In all three types, nuclei emit radiation, but the nature of that radiation differs from one type of decay to another. You can watch a video about the three types at this URL: (17:02). MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0718 | radioactive decay | T_3538 | Alpha decay occurs when an unstable nucleus emits an alpha particle and energy. The diagram in Figure 11.6 represents alpha decay. An alpha particle contains two protons and two neutrons, giving it a charge of +2. A helium nucleus has two protons and two neutrons, so an alpha particle is represented in nuclear equations by the symbol 4 He. 2 The superscript 4 is the mass number (2 protons + 2 neutrons). The subscript 2 is the charge of the particle as well as the number of protons. An example of alpha decay is the decay of uranium-238 to thorium-234. In this reaction, uranium loses two protons and two neutrons to become the element thorium. The reaction can be represented by this equation: 238 92 U 4 !234 90 Th +2 He + Energy If you count the number of protons and neutrons on each side of this equation, youll see that the numbers are the same on both sides of the arrow. This means that the equation is balanced. The thorium-234 produced in this reaction is unstable, so it will undergo radioactive decay as well. The alpha particle (42 He) produced in the reaction can pick up two electrons to form the element helium. This is how most of Earths helium formed. Problem Solving ? 4 Problem: Fill in the missing subscript and superscript to balance this nuclear equation: 208 84 Po !? Pb +2 He + Energy Solution: The subscript is 82, and the superscript is 204. You Try It! ? 4 Problem: Fill in the missing subscript and superscript to balance this nuclear equation: 222 ? Ra !86 Rn+2 He+Energy | text | null |
L_0718 | radioactive decay | T_3539 | Beta decay occurs when an unstable nucleus emits a beta particle and energy. A beta particle is an electron. It has a charge of -1. In nuclear equations, a beta particle is represented by the symbol 01 e. The subscript -1 represents the particles charge, and the superscript 0 shows that the particle has virtually no mass. Nuclei contain only protons and neutrons, so how can a nucleus emit an electron? A neutron first breaks down into a proton and an electron (see Figure 11.7). Then the electron is emitted from the nucleus, while the proton stays inside the nucleus. The proton increases the atomic number by one, thus changing one element into another. An example of beta decay is the decay of thorium-234 to protactinium-234. In this reaction, thorium loses a neutron and gains a proton to become protactinium. The reaction can be represented by this equation: 234 90 Th !234 91 Pa + 0 1 e + Energy The protactinium-234 produced in this reaction is radioactive and decays to another element. The electron produced in the reaction (plus another electron) can combine with an alpha particle to form helium. Problem Solving Problem: Fill in the missing subscript and superscript in this nuclear equation: 131 I 53 !?? Xe + 14 C ? !?7 N + Solution: The subscript is 54, and the superscript is 131. 0 e + Energy 1 You Try It! Problem: Fill in the missing subscript and superscript in this nuclear equation: 0 e + Energy 1 | text | null |
L_0718 | radioactive decay | T_3540 | In alpha and beta decay, both particles and energy are emitted. In gamma decay, only energy is emitted. Gamma decay occurs when an unstable nucleus gives off gamma rays. Gamma rays, like rays of visible light and X-rays, are waves of energy that travel through space at the speed of light. Gamma rays have the greatest amount of energy of all such waves. By itself, gamma decay doesnt cause one element to change into another, but it is released in nuclear reactions that do. Some of the energy released in alpha and beta decay is in the form of gamma rays. You can learn more about gamma radiation at this URL: (2:45). MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0718 | radioactive decay | T_3541 | The different types of radiation vary in how far they are able to travel and what they can penetrate (see Figure 11.8 and the URL below). MEDIA Click image to the left or use the URL below. URL: Alpha particles can travel only a few centimeters through air. They cannot pass through a sheet of paper or thin layer of clothing. They may burn the skin but cannot penetrate tissues beneath the skin. Beta particles can travel up to a meter through air. They can pass through paper and cloth but not through a sheet of aluminum. They can penetrate and damage tissues beneath the skin. Gamma rays can travel thousands of meters through air. They can pass through a sheet of aluminum as well as paper and cloth. They can be stopped only by several centimeters of lead or several meters of concrete. They can penetrate and damage organs deep inside the body. | text | null |
L_0718 | radioactive decay | T_3542 | A radioactive isotope decays at a certain constant rate. The rate is measured in a unit called the half-life. This is the length of time it takes for half of a given amount of the isotope to decay. The concept of half-life is illustrated in Figure 11.9 for the beta decay of phosphorus-32 to sulfur-32. The half-life of this radioisotope is 14 days. After 14 days, half of the original amount of phosphorus-32 has decayed. After another 14 days, half of the remaining amount (or one-quarter of the original amount) has decayed, and so on. Different radioactive isotopes vary greatly in their rate of decay. As you can see from the examples in Table 11.1, the half-life of a radioisotope can be as short as a split second or as long as several billion years. You can simulate radioactive decay of radioisotopes with different half-lives at the URL below. Some radioisotopes decay much more quickly than others. Isotope Uranium-238 Potassium-40 Carbon-14 Hydrogen-3 Radon-222 Polonium-214 Half-life 4.47 billion years 1.28 billion years 5,730 years 12.3 years 3.82 days 0.00016 seconds Problem Solving Problem: If you had a gram of carbon-14, how many years would it take for radioactive decay to reduce it to one-quarter of a gram? Solution: One gram would decay to one-quarter of a gram in 2 half-lives years. 1 2 12 = 1 4 , or 2 5,730 years = 11,460 You Try It! Problem: What fraction of a given amount of hydrogen-3 would be left after 36.9 years of decay? | text | null |
L_0718 | radioactive decay | T_3543 | Radioactive isotopes can be used to estimate the ages of fossils and rocks. The method is called radioactive dating. Carbon-14 dating is an example of radioactive dating. It is illustrated in the video at this URL: MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0718 | radioactive decay | T_3544 | Carbon-14 forms naturally in Earths atmosphere when cosmic rays strike atoms of nitrogen-14. Living things take in and use carbon-14, just as they do carbon-12. The carbon-14 in living things gradually decays to nitrogen-14. However, it is constantly replaced because living things keep taking in carbon-14. As a result, there is a fixed ratio of carbon-14 to carbon-12 in organisms as long as they are alive. This is illustrated in the top part of Figure 11.10. After organisms die, the carbon-14 they already contain continues to decay, but it is no longer replaced (see bottom part of Figure 11.10). Therefore, the carbon-14 in a dead organism constantly declines at a fixed rate equal to the half-life of carbon-14. Half of the remaining carbon-14 decays every 5,730 years. If you measure how much carbon- 14 is left in a fossil, you can determine how many half-lives (and how many years) have passed since the organism died. | text | null |
L_0718 | radioactive decay | T_3545 | Carbon-14 has a relatively short half-life (see Table 11.1). After about 50,000 years, too little carbon-14 is left in a fossil to be measured. Therefore, carbon-14 dating can only be used to date fossils that are less than 50,000 years old. Radioisotopes with a longer half-life, such as potassium-40, must be used to date older fossils and rocks. | text | null |
L_0719 | nuclear energy | T_3546 | Nuclear fission is the splitting of the nucleus of an atom into two smaller nuclei. This type of reaction releases a great deal of energy from a very small amount of matter. For example, nuclear fission of a tiny pellet of uranium-235, like the one pictured in Figure 11.11, can release as much energy as burning 1,000 kilograms of coal! Nuclear fission of uranium-235 can be represented by this equation: 235 92 U + 1 141 Neutron !92 36 Kr + 56 Ba + 3 Neutrons + Energy As shown in Figure 11.12, the reaction begins when a nucleus of uranium-235 absorbs a neutron. This can happen naturally or when a neutron is deliberately crashed into a uranium nucleus in a nuclear power plant. In either case, the nucleus of uranium becomes very unstable and splits in two. In this example, it forms krypton-92 and barium-141. The reaction also releases three neutrons and a great deal of energy. | text | null |
L_0719 | nuclear energy | T_3547 | The neutrons released in this nuclear fission reaction may be captured by other uranium nuclei and cause them to fission as well. This can start a nuclear chain reaction (see Figure 11.13). In a chain reaction, one fission reaction leads to others, which lead to others, and so on. A nuclear chain reaction is similar to a pile of wood burning. If you start one piece of wood burning, enough heat is produced by the burning wood to start the rest of the pile burning without any further help from you. You can see another example of a chain reaction at this URL: | text | null |
L_0719 | nuclear energy | T_3547 | The neutrons released in this nuclear fission reaction may be captured by other uranium nuclei and cause them to fission as well. This can start a nuclear chain reaction (see Figure 11.13). In a chain reaction, one fission reaction leads to others, which lead to others, and so on. A nuclear chain reaction is similar to a pile of wood burning. If you start one piece of wood burning, enough heat is produced by the burning wood to start the rest of the pile burning without any further help from you. You can see another example of a chain reaction at this URL: | text | null |
L_0719 | nuclear energy | T_3547 | The neutrons released in this nuclear fission reaction may be captured by other uranium nuclei and cause them to fission as well. This can start a nuclear chain reaction (see Figure 11.13). In a chain reaction, one fission reaction leads to others, which lead to others, and so on. A nuclear chain reaction is similar to a pile of wood burning. If you start one piece of wood burning, enough heat is produced by the burning wood to start the rest of the pile burning without any further help from you. You can see another example of a chain reaction at this URL: | text | null |
L_0719 | nuclear energy | T_3548 | If a nuclear chain reaction is uncontrolled, it produces a lot of energy all at once. This is what happens in an atomic bomb. If a nuclear chain reaction is controlled, it produces energy more slowly. This is what occurs in a nuclear power plant. The reaction may be controlled by inserting rods of material that do not undergo fission into the core of fissioning material (see Figure 11.14). The radiation from the controlled fission is used to heat water and turn it to steam. The steam is under pressure and causes a turbine to spin. The spinning turbine runs a generator, which produces electricity. | text | null |
L_0719 | nuclear energy | T_3549 | In the U.S., the majority of electricity is produced by burning coal or other fossil fuels. This causes air pollution, acid rain, and global warming. Fossil fuels are also limited and may eventually run out. Like fossil fuels, radioactive elements are limited. In fact, they are relatively rare, so they could run out sooner rather than later. On the other hand, nuclear fission does not release air pollution or cause the other environmental problems associated with burning fossil fuels. This is the major advantage of using nuclear fission as a source of energy. The main concern over the use of nuclear fission is the risk of radiation. Accidents at nuclear power plants can release harmful radiation that endangers people and other living things. Even without accidents, the used fuel that is left after nuclear fission reactions is still radioactive and very dangerous. It takes thousands of years for it to decay until it no longer releases harmful radiation. Therefore, used fuel must be stored securely to people and other living things. You can learn more about the problem of radioactive waste at this URL: | text | null |
L_0719 | nuclear energy | T_3550 | Nuclear fusion is the opposite of nuclear fission. In fusion, two or more small nuclei combine to form a single, larger nucleus. An example is shown in Figure 11.15. In this example, two hydrogen nuclei fuse to form a helium nucleus. A neutron and a great deal of energy are also released. In fact, fusion releases even more energy than fission does. | text | null |
L_0719 | nuclear energy | T_3551 | Nuclear fusion of hydrogen to form helium occurs naturally in the sun and other stars. It takes place only at extremely high temperatures. Thats because a great deal of energy is needed to overcome the force of repulsion between positively charged nuclei. The suns energy comes from fusion in its core, where temperatures reach millions of Kelvin (see Figure 11.16). | text | null |
L_0719 | nuclear energy | T_3552 | Scientists are searching for ways to create controlled nuclear fusion reactions on Earth. Their goal is develop nuclear fusion power plants, where the energy from fusion of hydrogen nuclei can be converted to electricity. How this might work is shown in Figure 11.17. The use of nuclear fusion for energy has several pros. Unlike nuclear fission, which involves dangerous radioiso- topes, nuclear fusion involves hydrogen and helium. These elements are harmless. Hydrogen is also very plentiful. There is a huge amount of hydrogen in ocean water. The hydrogen in just a gallon of water could produce as much energy by nuclear fusion as burning 1,140 liters (300 gallons) of gasoline! The hydrogen in the oceans would generate enough energy to supply all the worlds people for a very long time. Unfortunately, using energy from nuclear fusion is far from a reality. Scientists are a long way from developing the necessary technology. One problem is raising temperatures high enough for fusion to take place. Another problem is that matter this hot exists only in the plasma state. There are no known materials that can contain plasma, although a magnet might be able to do it. Thats because plasma consists of ions and responds to magnetism. You can learn more about research on nuclear fusion at the URL below. | text | null |
L_0719 | nuclear energy | T_3552 | Scientists are searching for ways to create controlled nuclear fusion reactions on Earth. Their goal is develop nuclear fusion power plants, where the energy from fusion of hydrogen nuclei can be converted to electricity. How this might work is shown in Figure 11.17. The use of nuclear fusion for energy has several pros. Unlike nuclear fission, which involves dangerous radioiso- topes, nuclear fusion involves hydrogen and helium. These elements are harmless. Hydrogen is also very plentiful. There is a huge amount of hydrogen in ocean water. The hydrogen in just a gallon of water could produce as much energy by nuclear fusion as burning 1,140 liters (300 gallons) of gasoline! The hydrogen in the oceans would generate enough energy to supply all the worlds people for a very long time. Unfortunately, using energy from nuclear fusion is far from a reality. Scientists are a long way from developing the necessary technology. One problem is raising temperatures high enough for fusion to take place. Another problem is that matter this hot exists only in the plasma state. There are no known materials that can contain plasma, although a magnet might be able to do it. Thats because plasma consists of ions and responds to magnetism. You can learn more about research on nuclear fusion at the URL below. | text | null |
L_0719 | nuclear energy | T_3553 | Probably the most famous equation in the world is E = mc2 . You may have heard of it. You may have even seen it on a tee shirt or coffee mug. Its a simple equation that was derived in 1905 by the physicist Albert Einstein (see Figure 11.18). Although the equation is simple, it is incredibly important. It changed how scientists view two of the most basic concepts in science: matter and energy. The equation shows that matter and energy are two forms of the same thing. It also shows how matter and energy are related. In addition, Einsteins equation explains why nuclear fission and nuclear fusion produce so much energy. You can listen to a recording of Einstein explaining his famous equation at this URL: | text | null |
L_0719 | nuclear energy | T_3554 | In Einsteins equation, the variable E stands for energy and the variable m stands for mass. The c in the equation is a constant. It stands for the speed of light. The speed of light is 300,000 kilometers (186,000 miles) per second, so c2 is a very big number, no matter what units are used to measure it. Einsteins equation means that the energy in a given amount of matter is equal to its mass times the square of the speed of light. Thats a huge amount of energy from even a tiny amount of mass. Suppose, for example, that you have 1 gram of matter. Thats about the mass of a paperclip. Multiplying that mass by the square of the speed of light yields enough energy to power 3,600 homes for a year! | text | null |
L_0719 | nuclear energy | T_3555 | When the nucleus of a radioisotope undergoes fission or fusion, it loses a tiny amount of mass. What happens to the lost mass? It isnt really lost at all. It is converted to energy. How much energy? E = mc2 . The change in mass is tiny, but it results in a great deal of energy. What about the laws of conservation of mass and conservation of energy? Do they not apply to nuclear reactions? We dont need to throw out these laws. Instead, we just need to combine them. It is more correct to say that the sum of mass and energy is always conserved in a nuclear reaction. Mass may change to energy, but the amount of mass and energy combined remains the same. | text | null |
L_0720 | distance and direction | T_3556 | Assume that a school bus, like the one in Figure 12.2, passes by as you stand on the sidewalk. Its obvious to you that the bus is moving. It is moving relative to you and the trees across the street. But what about to the children inside the bus? They arent moving relative to each other. If they look only at the other children sitting near them, they will not appear to be moving. They may only be able to tell that the bus is moving by looking out the window and seeing you and the trees whizzing by. This example shows that how we perceive motion depends on our frame of reference. Frame of reference refers to something that is not moving with respect to an observer that can be used to detect motion. For the children on the bus, if they use other children riding the bus as their frame of reference, they do not appear to be moving. But if they use objects outside the bus as their frame of reference, they can tell they are moving. What is your frame of reference if you are standing on the sidewalk and see the bus go by? How can you tell the bus is moving? The video at the URL below illustrates other examples of how frame of reference is related to motion. MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0720 | distance and direction | T_3556 | Assume that a school bus, like the one in Figure 12.2, passes by as you stand on the sidewalk. Its obvious to you that the bus is moving. It is moving relative to you and the trees across the street. But what about to the children inside the bus? They arent moving relative to each other. If they look only at the other children sitting near them, they will not appear to be moving. They may only be able to tell that the bus is moving by looking out the window and seeing you and the trees whizzing by. This example shows that how we perceive motion depends on our frame of reference. Frame of reference refers to something that is not moving with respect to an observer that can be used to detect motion. For the children on the bus, if they use other children riding the bus as their frame of reference, they do not appear to be moving. But if they use objects outside the bus as their frame of reference, they can tell they are moving. What is your frame of reference if you are standing on the sidewalk and see the bus go by? How can you tell the bus is moving? The video at the URL below illustrates other examples of how frame of reference is related to motion. MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0720 | distance and direction | T_3557 | Did you ever go to a track meet like the one pictured in Figure 12.3? Running events in track include 100-meter sprints and 2000-meter races. Races are named for their distance. Distance is the length of the route between two points. The length of the route in a race is the distance between the starting and finishing lines. In a 100-meter sprint, for example, the distance is 100 meters. | text | null |
L_0720 | distance and direction | T_3558 | The SI unit for distance is the meter (1 m = 3.28 ft). Short distances may be measured in centimeters (1 cm = 0.01 m). Long distances may be measured in kilometers (1 km = 1000 m). For example, you might measure the distance a frogs tongue moves in centimeters and the distance a cheetah moves in kilometers. | text | null |
L_0720 | distance and direction | T_3559 | Maps can often be used to measure distance. Look at the map in Figure 12.4. Find Mias house and the school. You can use the map key to directly measure the distance between these two points. The distance is 2 kilometers. Measure it yourself to see if you agree. | text | null |
L_0720 | distance and direction | T_3560 | Things dont always move in straight lines like the route from Mias house to the school. Sometimes they change direction as they move. For example, the route from Mias house to the post office changes from west to north at the school (see Figure 12.4). To find the total distance of a route that changes direction, you must add up the distances traveled in each direction. From Mias house to the school, for example, the distance is 2 kilometers. From the school to the post office, the distance is 1 kilometer. Therefore, the total distance from Mias house to the post office is 3 kilometers. You Try It! Problem: What is the distance from the post office to the park in Figure 12.4? Direction is just as important as distance in describing motion. For example, if Mia told a friend how to reach the post office from her house, she couldnt just say, "go 3 kilometers." The friend might end up at the park instead of the post office. Mia would have to be more specific. She could say, "go west for 2 kilometers and then go north for 1 kilometer." When both distance and direction are considered, motion is a vector. A vector is a quantity that includes both size and direction. A vector is represented by an arrow. The length of the arrow represents distance. The way the arrow points shows direction. The red arrows in Figure 12.4 are vectors for Mias route to the school and post office. If you want to learn more about vectors, watch the videos at these URLs: (5:27) MEDIA Click image to the left or use the URL below. URL: You Try It! Problem: Draw vectors to represent the route from the post office to the park in Figure 12.4. | text | null |
L_0721 | speed and velocity | T_3561 | Speed is an important aspect of motion. It is a measure of how fast or slow something moves. It depends on how far something travels and how long it takes to travel that far. Speed can be calculated using this general formula: speed = distance time A familiar example is the speed of a car. In the U.S., this is usually expressed in miles per hour (see Figure 12.6). If your family makes a car trip that covers 120 miles and takes 3 hours, then the cars speed is: speed = 120 mi = 40 mi/h 3h The speed of a car may also be expressed in kilometers per hour (km/h). The SI unit for speed is meters per second (m/s). | text | null |
L_0721 | speed and velocity | T_3562 | When you travel by car, you usually dont move at a constant speed. Instead you go faster or slower depending on speed limits, traffic, traffic lights, and many other factors. For example, you might travel 65 miles per hour on a highway but only 20 miles per hour on a city street (see Figure 12.7). You might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars. The speed of a moving car or other object at a given instant is called its instantaneous speed. It may vary from moment to moment, so it is hard to calculate. Its easier to calculate the average speed of a moving object than the instantaneous speed. The average speed is the total distance traveled divided by the total time it took to travel that distance. To calculate the average speed, you can use the general formula for speed that was given above. Suppose, for example, that you took a 75-mile car trip with your family. Your instantaneous speed would vary throughout the trip. If the trip took a total of 1.5 hours, your average speed for the trip would be: average speed = 75 mi = 50 mi/h 1.5 h You can see a video about instantaneous and average speed and how to calculate them at this URL: MEDIA Click image to the left or use the URL below. URL: You Try It! Problem: Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri 15 minutes to make the round trip. What was her average speed for the entire trip? | text | null |
L_0721 | speed and velocity | T_3563 | The motion of an object can be represented by a distance-time graph like the one in Figure 12.8. A distance-time graph shows how the distance from the starting point changes over time. The graph in Figure 12.8 represents a bike trip. The trip began at 7:30 AM (A) and ended at 12:30 PM (F). The rider traveled from the starting point to a destination and then returned to the starting point again. | text | null |
L_0721 | speed and velocity | T_3564 | In a distance-time graph, the speed of the object is represented by the slope, or steepness, of the graph line. If the line is straight, like the line between A and B in Figure 12.8, then the speed is constant. The average speed can be calculated from the graph. The change in distance (represented by Dd) divided by the change in time (represented by Dt): speed = Dd Dt For example, the speed between A and B in Figure 12.8 is: speed = Dd 20 km 0 km 20 km = = = 20 km/h Dt 8:30 7:30 h 1h If the graph line is horizontal, as it is between B and C, then the slope and the speed are zero: speed = Dd 20 km 20 km 0 km = = = 0 km/h Dt 9:00 8:30 h 0.5 h You Try It! Problem: In Figure 12.8, calculate the speed of the rider between C and D. | text | null |
L_0721 | speed and velocity | T_3565 | If you know the speed of a moving object, you can also calculate the distance it will travel in a given amount of time. To do so, you would use this version of the general speed formula: distance = speed time For example, if a car travels at a speed of 60 km/h for 2 hours, then the distance traveled is: distance = 60 km/h 2 h = 120 km You Try It! Problem: If Maria runs at a speed of 2 m/s, how far will she run in 60 seconds? | text | null |
L_0721 | speed and velocity | T_3566 | Speed tells you only how fast an object is moving. It doesnt tell you the direction the object is moving. The measure of both speed and direction is called velocity. Velocity is a vector that can be represented by an arrow. The length of the arrow represents speed, and the way the arrow points represents direction. The three arrows in Figure directions. They represent objects moving at the same speed but in different directions. Vector C is shorter than vector A or B but points in the same direction as vector A. It represents an object moving at a slower speed than A or B but in the same direction as A. If youre still not sure of the difference between speed and velocity, watch the cartoon at this URL: (2:10). MEDIA Click image to the left or use the URL below. URL: In general, if two objects are moving at the same speed and in the same direction, they have the same velocity. If two objects are moving at the same speed but in different directions (like A and B in Figure 12.9), they have different velocities. If two objects are moving in the same direction but at a different speed (like A and C in Figure 12.9), they have different velocities. A moving object that changes direction also has a different velocity, even if its speed does not change. | text | null |
L_0722 | acceleration | T_3567 | Acceleration is a measure of the change in velocity of a moving object. It shows how quickly velocity changes. Acceleration may reflect a change in speed, a change in direction, or both. Because acceleration includes both a size (speed) and direction, it is a vector. People commonly think of acceleration as an increase in speed, but a decrease in speed is also acceleration. In this case, acceleration is negative. Negative acceleration may be called deceleration. A change in direction without a change in speed is acceleration as well. You can see several examples of acceleration in Figure 12.11. If you are accelerating, you may be able to feel the change in velocity. This is true whether you change your speed or your direction. Think about what it feels like to ride in a car. As the car speeds up, you feel as though you are being pressed against the seat. The opposite occurs when the car slows down, especially if the change in speed is | text | null |
L_0722 | acceleration | T_3568 | Calculating acceleration is complicated if both speed and direction are changing. Its easier to calculate acceleration when only speed is changing. To calculate acceleration without a change in direction, you just divide the change in velocity (represented by Dv) by the change in time (represented by Dt). The formula for acceleration in this case is: Acceleration = Dv Dt Consider this example. The cyclist in Figure 12.12 speeds up as he goes downhill on this straight trail. His velocity changes from 1 meter per second at the top of the hill to 6 meters per second at the bottom. If it takes 5 seconds for him to reach the bottom, what is his acceleration, on average, as he flies down the hill? Acceleration = Dv 6 m/s 1 m/s 5 m/s 1 m/s = = = = 1 m/s2 Dt 5s 5s 1m In words, this means that for each second the cyclist travels downhill, his velocity increases by 1 meter per second (on average). The answer to this problem is expressed in the SI unit for acceleration: m/s2 ("meters per second squared"). You Try It! Problem: Tranh slowed his skateboard as he approached the street. He went from 8 m/s to 2 m/s in a period of 3 seconds. What was his acceleration? | text | null |
L_0722 | acceleration | T_3569 | The acceleration of an object can be represented by a velocity-time graph like the one in Figure 12.13. A velocity- time graph shows how velocity changes over time. It is similar to a distance-time graph except the y axis represents velocity instead of distance. The graph in Figure 12.13 represents the velocity of a sprinter on a straight track. The runner speeds up for the first 4 seconds of the race, then runs at a constant velocity for the next 3 seconds, and finally slows to a stop during the last 3 seconds of the race. In a velocity-time graph, acceleration is represented by the slope of the graph line. If the line slopes upward, like the line between A and B in Figure 12.13, velocity is increasing, so acceleration is positive. If the line is horizontal, as it is between B and C, velocity is not changing, so acceleration is zero. If the line slopes downward, like the line between C and D, velocity is decreasing, so acceleration is negative. You can review the concept of acceleration as well as other chapter concepts by watching the musical video at this URL: | text | null |
L_0723 | what is force | T_3570 | Force is defined as a push or a pull acting on an object. Examples of forces include friction and gravity. Both are covered in detail later in this chapter. Another example of force is applied force. It occurs when a person or thing applies force to an object, like the girl pushing the swing in Figure 13.1. The force of the push causes the swing to move. | text | null |
L_0723 | what is force | T_3571 | Force is a vector because it has both size and direction. For example, the girl in Figure 13.1 is pushing the swing away from herself. Thats the direction of the force. She can give the swing a strong push or a weak push. Thats the size, or strength, of the force. Like other vectors, forces can be represented with arrows. Figure 13.2 shows some examples. The length of each arrow represents the strength of the force, and the way the arrow points represents the direction of the force. How could you use an arrow to represent the girls push on the swing in Figure 13.1? | text | null |
L_0723 | what is force | T_3571 | Force is a vector because it has both size and direction. For example, the girl in Figure 13.1 is pushing the swing away from herself. Thats the direction of the force. She can give the swing a strong push or a weak push. Thats the size, or strength, of the force. Like other vectors, forces can be represented with arrows. Figure 13.2 shows some examples. The length of each arrow represents the strength of the force, and the way the arrow points represents the direction of the force. How could you use an arrow to represent the girls push on the swing in Figure 13.1? | text | null |
L_0723 | what is force | T_3572 | The SI unit of force is the newton (N). One newton is the amount of force that causes a mass of 1 kilogram to accelerate at 1 m/s2 . Thus, the newton can also be expressed as kgm/s2 . The newton was named for the scientist Sir Isaac Newton, who is famous for his law of gravity. Youll learn more about Sir Isaac Newton later in the chapter. | text | null |
L_0723 | what is force | T_3573 | More than one force may act on an object at the same time. In fact, just about all objects on Earth have at least two forces acting on them at all times. One force is gravity, which pulls objects down toward the center of Earth. The other force is an upward force that may be provided by the ground or other surface. Consider the example in Figure 13.3. A book is resting on a table. Gravity pulls the book downward with a force of 20 newtons. At the same time, the table pushes the book upward with a force of 20 newtons. The combined forces acting on the book or any other object are called the net force. This is the overall force acting on an object that takes into account all of the individual forces acting on the object. You can learn more about the concept of net force at this URL: . | text | null |
L_0723 | what is force | T_3574 | When two forces act on an object in opposite directions, like the book on the table, the net force is equal to the difference between the two forces. In other words, one force is subtracted from the other to calculate the net force. If the opposing forces are equal in strength, the net force is zero. Thats what happens with the book on the table. The upward force minus the downward force equals zero (20 N up - 20 N down = 0 N). Because the forces on the book are balanced, the book remains on the table and doesnt move. In addition to these downward and upward forces, which generally cancel each other out, forces may push or pull an object in other directions. Look at the dogs playing tug-of-war in Figure 13.4. One dog is pulling on the rope with a force of 10 newtons to the left. The other dog is pulling on the rope with a force of 12 newtons to the right. These opposing forces are not equal in strength, so they are unbalanced. When opposing forces are unbalanced, the net force is greater than zero. The net force on the rope is 2 newtons to the right, so the rope will move to the right. | text | null |
L_0723 | what is force | T_3575 | Two forces may act on an object in the same direction. You can see an example of this in Figure 13.5. After the man on the left lifts up the couch, he will push the couch to the right with a force of 25 newtons. At the same time, the man to the right is pulling the couch to the right with a force of 20 newtons. When two forces act in the same direction, the net force is equal to the sum of the forces. This always results in a stronger force than either of the individual forces alone. In this case, the net force on the couch is 45 newtons to the right, so the couch will move to the right. You Try It! Problem: The boys in the drawing above are about to kick the soccer ball in opposite directions. What will be the net force on the ball? In which direction will the ball move? | text | null |
L_0723 | what is force | T_3575 | Two forces may act on an object in the same direction. You can see an example of this in Figure 13.5. After the man on the left lifts up the couch, he will push the couch to the right with a force of 25 newtons. At the same time, the man to the right is pulling the couch to the right with a force of 20 newtons. When two forces act in the same direction, the net force is equal to the sum of the forces. This always results in a stronger force than either of the individual forces alone. In this case, the net force on the couch is 45 newtons to the right, so the couch will move to the right. You Try It! Problem: The boys in the drawing above are about to kick the soccer ball in opposite directions. What will be the net force on the ball? In which direction will the ball move? | text | null |
L_0724 | friction | T_3576 | Friction is a force that opposes motion between two surfaces that are touching. Friction can work for or against us. For example, putting sand on an icy sidewalk increases friction so you are less likely to slip. On the other hand, too much friction between moving parts in a car engine can cause the parts to wear out. Other examples of friction are illustrated in Figure 13.7. You can see an animation showing how friction opposes motion at this URL: http://w | text | null |
L_0724 | friction | T_3577 | Friction occurs because no surface is perfectly smooth. Even surfaces that look smooth to the unaided eye appear rough or bumpy when viewed under a microscope. Look at the metal surfaces in Figure 13.8. The metal foil is so smooth that it is shiny. However, when highly magnified, the surface of metal appears to be very bumpy. All those mountains and valleys catch and grab the mountains and valleys of any other surface that contacts the metal. This creates friction. | text | null |
L_0724 | friction | T_3578 | Rougher surfaces have more friction between them than smoother surfaces. Thats why we put sand on icy sidewalks and roads. The blades of skates are much smoother than the soles of shoes. Thats why you cant slide as far across ice with shoes as you can with skates (see Figure 13.9). The rougher surface of shoes causes more friction and slows you down. Heavier objects also have more friction because they press together with greater force. Did you ever try to push boxes or furniture across the floor? Its harder to overcome friction between heavier objects and the floor than it is between lighter objects and the floor. | text | null |
L_0724 | friction | T_3579 | You know that friction produces heat. Thats why rubbing your hands together makes them warmer. But do you know why the rubbing produces heat? Friction causes the molecules on rubbing surfaces to move faster, so they have more heat energy. Heat from friction can be useful. It not only warms your hands. It also lets you light a match (see Figure 13.10). On the other hand, heat from friction can be a problem inside a car engine. It can cause the car to overheat. To reduce friction, oil is added to the engine. Oil coats the surfaces of moving parts and makes them slippery so there is less friction. | text | null |
L_0724 | friction | T_3580 | There are different ways you could move heavy boxes. You could pick them up and carry them. You could slide them across the floor. Or you could put them on a dolly like the one in Figure 13.11 and roll them across the floor. This example illustrates three types of friction: static friction, sliding friction, and rolling friction. Another type of friction is fluid friction. All four types of friction are described below. In each type, friction works opposite the direction of the force applied to a move an object. You can see a video demonstration of the different types of friction at this URL: (1:07). | text | null |
L_0724 | friction | T_3581 | Static friction acts on objects when they are resting on a surface. For example, if you are walking on a sidewalk, there is static friction between your shoes and the concrete each time you put down your foot (see Figure 13.12). Without this static friction, your feet would slip out from under you, making it difficult to walk. Static friction also allows you to sit in a chair without sliding to the floor. Can you think of other examples of static friction? | text | null |
L_0724 | friction | T_3582 | Sliding friction is friction that acts on objects when they are sliding over a surface. Sliding friction is weaker than static friction. Thats why its easier to slide a piece of furniture over the floor after you start it moving than it is to get it moving in the first place. Sliding friction can be useful. For example, you use sliding friction when you write with a pencil and when you put on your bikes brakes. | text | null |
L_0724 | friction | T_3583 | Rolling friction is friction that acts on objects when they are rolling over a surface. Rolling friction is much weaker than sliding friction or static friction. This explains why it is much easier to move boxes on a wheeled dolly than by carrying or sliding them. It also explains why most forms of ground transportation use wheels, including cars, 4-wheelers, bicycles, roller skates, and skateboards. Ball bearings are another use of rolling friction (see Figure | text | null |
L_0724 | friction | T_3584 | Fluid friction is friction that acts on objects that are moving through a fluid. A fluid is a substance that can flow and take the shape of its container. Fluids include liquids and gases. If youve ever tried to push your open hand through the water in a tub or pool, then youve experienced fluid friction between your hand and the water. When a skydiver is falling toward Earth with a parachute, fluid friction between the parachute and the air slows the descent (see Figure 13.14). Fluid pressure with the air is called air resistance. The faster or larger a moving object is, the greater is the fluid friction resisting its motion. The very large surface area of a parachute, for example, has greater air resistance than a skydivers body. | text | null |
L_0725 | gravity | T_3585 | Gravity has traditionally been defined as a force of attraction between two masses. According to this conception of gravity, anything that has mass, no matter how small, exerts gravity on other matter. The effect of gravity is that objects exert a pull on other objects. Unlike friction, which acts only between objects that are touching, gravity also acts between objects that are not touching. In fact, gravity can act over very long distances. | text | null |
L_0725 | gravity | T_3586 | You are already very familiar with Earths gravity. It constantly pulls you toward the center of the planet. It prevents you and everything else on Earth from being flung out into space as the planet spins on its axis. It also pulls objects above the surface, from meteors to skydivers, down to the ground. Gravity between Earth and the moon and between Earth and artificial satellites keeps all these objects circling around Earth. Gravity also keeps Earth moving around the sun. | text | null |
L_0725 | gravity | T_3587 | Weight measures the force of gravity pulling on an object. Because weight measures force, the SI unit for weight is the newton (N). On Earth, a mass of 1 kilogram has a weight of about 10 newtons because of the pull of Earths gravity On the moon, which has less gravity, the same mass would weigh less. Weight is measured with a scale, like the spring scale in Figure 13.16. The scale measures the force with which gravity pulls an object downward. | text | null |
L_0725 | gravity | T_3588 | People have known about gravity for thousands of years. After all, they constantly experienced gravity in their daily lives. They knew that things always fall toward the ground. However, it wasnt until Sir Isaac Newton developed his law of gravity in the late 1600s that people really began to understand gravity. Newton is pictured in Figure 13.17. | text | null |
L_0725 | gravity | T_3589 | Newton was the first one to suggest that gravity is universal and affects all objects in the universe. Thats why his law of gravity is called the law of universal gravitation. Universal gravitation means that the force that causes an apple to fall from a tree to the ground is the same force that causes the moon to keep moving around Earth. Universal gravitation also means that while Earth exerts a pull on you, you exert a pull on Earth. In fact, there is gravity between you and every mass around you your desk, your book, your pen. Even tiny molecules of gas are attracted to one another by the force of gravity. Newtons law had a huge impact on how people thought about the universe. It explains the motion of objects not only on Earth but in outer space as well. You can learn more about Newtons law of gravity in the video at this URL: | text | null |
L_0725 | gravity | T_3590 | Newtons law also states that the strength of gravity between any two objects depends on two factors: the masses of the objects and the distance between them. Objects with greater mass have a stronger force of gravity. For example, because Earth is so massive, it attracts you and your desk more strongly than you and your desk attract each other. Thats why you and the desk remain in place on the floor rather than moving toward one another. Objects that are closer together have a stronger force of gravity. For example, the moon is closer to Earth than it is to the more massive sun, so the force of gravity is greater between the moon and Earth than between the moon and the sun. Thats why the moon circles around Earth rather than the sun. This is illustrated in Figure You can apply these relationships among mass, distance, and gravity by designing your own roller coaster at this URL: . | text | null |
L_0725 | gravity | T_3591 | Newtons idea of gravity can predict the motion of most but not all objects. In the early 1900s, Albert Einstein came up with a theory of gravity that is better at predicting how all objects move. Einstein showed mathematically that gravity is not really a force in the sense that Newton thought. Instead, gravity is a result of the warping, or curving, of space and time. Imagine a bowling ball pressing down on a trampoline. The surface of the trampoline would curve downward instead of being flat. Einstein theorized that Earth and other very massive bodies affect space and time around them in a similar way. This idea is represented in Figure 13.19. According to Einstein, objects curve toward one another because of the curves in space and time, not because they are pulling on each other with a force of attraction as Newton thought. You can see an animation of Einsteins theory of gravity at this URL: http://einstein. theory of gravity, go to this URL: | text | null |
L_0725 | gravity | T_3591 | Newtons idea of gravity can predict the motion of most but not all objects. In the early 1900s, Albert Einstein came up with a theory of gravity that is better at predicting how all objects move. Einstein showed mathematically that gravity is not really a force in the sense that Newton thought. Instead, gravity is a result of the warping, or curving, of space and time. Imagine a bowling ball pressing down on a trampoline. The surface of the trampoline would curve downward instead of being flat. Einstein theorized that Earth and other very massive bodies affect space and time around them in a similar way. This idea is represented in Figure 13.19. According to Einstein, objects curve toward one another because of the curves in space and time, not because they are pulling on each other with a force of attraction as Newton thought. You can see an animation of Einsteins theory of gravity at this URL: http://einstein. theory of gravity, go to this URL: | text | null |
L_0725 | gravity | T_3592 | Regardless of what gravity is a force between masses or the result of curves in space and time the effects of gravity on motion are well known. You already know that gravity causes objects to fall down to the ground. Gravity affects the motion of objects in other ways as well. | text | null |
L_0725 | gravity | T_3593 | When gravity pulls objects toward the ground, it causes them to accelerate. Acceleration due to gravity equals 9.8 m/s2 . In other words, the velocity at which an object falls toward Earth increases each second by 9.8 m/s. Therefore, after 1 second, an object is falling at a velocity of 9.8 m/s. After 2 seconds, it is falling at a velocity of 19.6 m/s (9.8 m/s 2), and so on. This is illustrated in Figure 13.20. You can compare the acceleration due to gravity on Earth, the moon, and Mars with the interactive animation called "Freefall" at this URL: http://jersey.uoregon.edu/vlab/ . You might think that an object with greater mass would accelerate faster than an object with less mass. After all, its greater mass means that it is pulled by a stronger force of gravity. However, a more massive object accelerates at the same rate as a less massive object. The reason? The more massive object is harder to move because of its greater mass. As a result, it ends up moving at the same acceleration as the less massive object. Consider a bowling ball and a basketball. The bowling ball has greater mass than the basketball. However, if you were to drop both balls at the same time from the same distance above the ground, they would reach the ground together. This is true of all falling objects, unless air resistance affects one object more than another. For example, a falling leaf is slowed down by air resistance more than a falling acorn because of the leafs greater surface area. However, if the leaf and acorn were to fall in the absence of air (that is, in a vacuum), they would reach the ground at the same time. | text | null |
L_0725 | gravity | T_3594 | Earths gravity also affects the acceleration of objects that start out moving horizontally, or parallel to the ground. Look at Figure 13.21. A cannon shoots a cannon ball straight ahead, giving the ball horizontal motion. At the same time, gravity pulls the ball down toward the ground. Both forces acting together cause the ball to move in a curved path. This is called projectile motion. Projectile motion also applies to other moving objects, such as arrows shot from a bow. To hit the bulls eye of a target with an arrow, you actually have to aim for a spot above the bulls eye. Thats because by the time the arrow reaches the target, it has started to curve downward toward the ground. Figure 13.22 shows what happens if you aim at the bulls eye instead of above it. You can access interactive animations of projectile motion at these URLs: http://phet.colorado.edu/en/simulation/projectile-motion http://jersey.uoregon.edu/vlab/ (Select the applet entitled Cannon.) | text | null |
L_0725 | gravity | T_3595 | The moon moves around Earth in a circular path called an orbit. Why doesnt Earths gravity pull the moon down to the ground instead? The moon has enough forward velocity to partly counter the force of Earths gravity. It constantly falls toward Earth, but it stays far enough away from Earth so that it actually falls around the planet. As a result, the moon keeps orbiting Earth and never crashes into it. The diagram in Figure 13.23 shows how this happens. You can explore gravity and orbital motion in depth with the animation at this URL: http://phet.colorado You can see an animated version of this diagram at: http://en.wikipedia.org/wiki/File:Orbital_motion.gif . | text | null |
L_0725 | gravity | T_3595 | The moon moves around Earth in a circular path called an orbit. Why doesnt Earths gravity pull the moon down to the ground instead? The moon has enough forward velocity to partly counter the force of Earths gravity. It constantly falls toward Earth, but it stays far enough away from Earth so that it actually falls around the planet. As a result, the moon keeps orbiting Earth and never crashes into it. The diagram in Figure 13.23 shows how this happens. You can explore gravity and orbital motion in depth with the animation at this URL: http://phet.colorado You can see an animated version of this diagram at: http://en.wikipedia.org/wiki/File:Orbital_motion.gif . | text | null |
L_0726 | elastic force | T_3596 | Something that is elastic can return to its original shape after being stretched or compressed. This property is called elasticity. As you stretch or compress an elastic material, it resists the change in shape. It exerts a counter force in the opposite direction. This force is called elastic force. Elastic force causes the material to spring back to its original shape as soon as the stretching or compressing force is released. You can watch a demonstration of elastic force at this URL: (3:57). MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0726 | elastic force | T_3597 | Elastic force can be very useful. You probably use it yourself every day. A few common uses of elastic force are pictured in Figure 13.25. Did you ever use a resistance band like the one in the figure? When you pull on the band, it stretches but doesnt break. The resistance you feel when you pull on it is elastic force. The resistance of the band to stretching is what gives your muscles a workout. After you stop pulling on the band, it returns to its original shape, ready for the next workout. Springs like the ones in Figure 13.26 also have elastic force when they are stretched or compressed. And like stretchy materials, they return to their original shape when the stretching or compressing force is released. Because of these properties, springs are used in scales to measure weight. They also cushion the ride in a car and provide springy support beneath a mattress. Can you think of other uses of springs? | text | null |
L_0727 | newtons first law | T_3598 | Newtons first law of motion states that an objects motion will not change unless an unbalanced force acts on the object. If the object is at rest, it will stay at rest. If the object is in motion, it will stay in motion and its velocity will remain the same. In other words, neither the direction nor the speed of the object will change as long as the net force acting on it is zero. You can watch a video about Newtons first law at this URL: http://videos.howstuffworks.com/ Look at the pool balls in Figure 14.2. When a pool player pushes the pool stick against the white ball, the white ball is set into motion. Once the white ball is rolling, it rolls all the way across the table and stops moving only after it crashes into the cluster of colored balls. Then, the force of the collision starts the colored balls moving. Some may roll until they bounce off the raised sides of the table. Some may fall down into the holes at the edges of the table. None of these motions will occur, however, unless that initial push of the pool stick is applied. As long as the net force on the balls is zero, they will remain at rest. | text | null |
L_0727 | newtons first law | T_3599 | Newtons first law of motion is also called the law of inertia. Inertia is the tendency of an object to resist a change in its motion. If an object is already at rest, inertia will keep it at rest. If the object is already moving, inertia will keep it moving. Think about what happens when you are riding in a car that stops suddenly. Your body moves forward on the seat. Why? The brakes stop the car but not your body, so your body keeps moving forward because of inertia. Thats why its important to always wear a seat belt. Inertia also explains the amusement park ride in Figure 14.1. The car keeps changing direction, but the riders keep moving in the same direction as before. They slide to the opposite side of the car as a result. You can see an animation of inertia at this URL: | text | null |
L_0727 | newtons first law | T_3600 | The inertia of an object depends on its mass. Objects with greater mass also have greater inertia. Think how hard it would be to push a big box full of books, like the one in Figure 14.3. Then think how easy it would be to push the box if it was empty. The full box is harder to move because it has greater mass and therefore greater inertia. | text | null |
L_0727 | newtons first law | T_3601 | To change the motion of an object, inertia must be overcome by an unbalanced force acting on the object. Until the soccer player kicks the ball in Figure 14.4, the ball remains motionless on the ground. However, when the ball is kicked, the force on it is suddenly unbalanced. The ball starts moving across the field because its inertia has been overcome. | text | null |
L_0728 | newtons second law | T_3602 | Newton determined that two factors affect the acceleration of an object: the net force acting on the object and the objects mass. The relationships between these two factors and motion make up Newtons second law of motion. This law states that the acceleration of an object equals the net force acting on the object divided by the objects mass. This can be represented by the equation: Net force , or Mass F a= m Acceleration = You can watch a video about how Newtons second law of motion applies to football at this URL: http://science36 | text | null |
L_0728 | newtons second law | T_3603 | Newtons second law shows that there is a direct relationship between force and acceleration. The greater the force that is applied to an object of a given mass, the more the object will accelerate. For example, doubling the force on the object doubles its acceleration. The relationship between mass and acceleration, on the other hand, is an inverse relationship. The greater the mass of an object, the less it will accelerate when a given force is applied. For example, doubling the mass of an object results in only half as much acceleration for the same amount of force. Consider the example of a batter, like the boy in Figure 14.6. The harder he hits the ball, the greater will be its acceleration. It will travel faster and farther if he hits it with more force. What if the batter hits a baseball and a softball with the same amount of force? The softball will accelerate less than the baseball because the softball has greater mass. As a result, it wont travel as fast or as far as the baseball. | text | null |
L_0728 | newtons second law | T_3604 | The equation for acceleration given above can be used to calculate the acceleration of an object that is acted on by an unbalanced force. For example, assume you are pushing a large wooden trunk, like the one shown in Figure acceleration of the trunk, substitute these values in the equation for acceleration: a= F 20 N 2N = = m 10 kg kg Recall that one newton (1 N) is the force needed to cause a 1-kilogram mass to accelerate at 1 m/s2 . Therefore, force can also be expressed in the unit kgm/s2 . This way of expressing force can be substituted for newtons in the solution to the problem: a= 2 N 2 kg m/s2 = = 2 m/s2 kg kg Why are there no kilograms in the final answer to this problem? The kilogram units in the numerator and denominator of the fraction cancel out. As a result, the answer is expressed in the correct units for acceleration: m/s2 . You Try It! Problem: Assume that you add the weights to the trunk in Figure 14.7. If you push the trunk and weights with a force of 20 N, what will be the trunks acceleration? Need more practice? You can find additional problems at this URL: | text | null |
L_0728 | newtons second law | T_3605 | Newtons second law of motion explains the weight of objects. Weight is a measure of the force of gravity pulling on an object of a given mass. Its the force (F) in the acceleration equation that was introduced above: a= F m This equation can also be written as: F = ma The acceleration due to gravity of an object equals 9.8 m/s2 , so if you know the mass of an object, you can calculate its weight as: F = m 9.8 m/s2 As this equation shows, weight is directly related to mass. As an objects mass increases, so does its weight. For example, if mass doubles, weight doubles as well. You can learn more about weight and acceleration at this URL: Problem Solving Problem: Daisy has a mass of 35 kilograms. How much does she weigh? Solution: Use the formula: F = m 9.8 m/s2 . F = 35 kg 9.8 m/s2 = 343.0 kg m/s2 = 343.0 N You Try It! Problem: Daisys dad has a mass is 70 kg, which is twice Daisys mass. Predict how much Daisys dad weighs. Then calculate his weight to see if your prediction is correct. Helpful Hints The equation for calculating weight (F = m a) works only when the correct units of measurement are used. Mass must be in kilograms (kg). Acceleration must be in m/s2 . Weight (F) is expressed in kgm/s2 or in newtons (N). | text | null |
L_0729 | newtons third law | T_3606 | Newtons third law of motion states that every action has an equal and opposite reaction. This means that forces always act in pairs. First an action occurs, such as the skateboarders pushing together. Then a reaction occurs that is equal in strength to the action but in the opposite direction. In the case of the skateboarders, they move apart, and the distance they move depends on how hard they first pushed together. You can see other examples of actions and reactions in Figure 14.9. You can watch a video about actions and reactions at this URL: You might think that actions and reactions would cancel each other out like balanced forces do. Balanced forces, which are also equal and opposite, cancel each other out because they act on the same object. Action and reaction forces, in contrast, act on different objects, so they dont cancel each other out and, in fact, often result in motion. For example, in Figure 14.9, the kangaroos action acts on the ground, but the grounds reaction acts on the kangaroo. As a result, the kangaroo jumps away from the ground. One of the action-reaction examples in the Figure 14.9 does not result in motion. Do you know which one it is? | text | null |
L_0729 | newtons third law | T_3607 | What if a friend asked you to play catch with a bowling ball, like the one pictured in Figure 14.10? Hopefully, you would refuse to play! A bowling ball would be too heavy to catch without risk of injury assuming you could even throw it. Thats because a bowling ball has a lot of mass. This gives it a great deal of momentum. Momentum is a property of a moving object that makes the object hard to stop. It equals the objects mass times its velocity. It can be represented by the equation: Momentum = Mass Velocity This equation shows that momentum is directly related to both mass and velocity. An object has greater momentum if it has greater mass, greater velocity, or both. For example, a bowling ball has greater momentum than a softball when both are moving at the same velocity because the bowling ball has greater mass. However, a softball moving at a very high velocity say, 100 miles an hour would have greater momentum than a slow-rolling bowling ball. If an object isnt moving at all, it has no momentum. Thats because its velocity is zero, and zero times anything is zero. | text | null |
L_0729 | newtons third law | T_3608 | Momentum can be calculated by multiplying an objects mass in kilograms (kg) by its velocity in meters per second (m/s). For example, assume that a golf ball has a mass of 0.05 kg. If the ball is traveling at a velocity of 50 m/s, its momentum is: Momentum = 0.05 kg 50 m/s = 2.5 kg m/s Note that the SI unit for momentum is kgm/s. Problem Solving Problem: What is the momentum of a 40-kg child who is running straight ahead with a velocity of 2 m/s? Solution: The child has momentum of: 40 kg 2 m/s = 80 kgm/s. You Try It! Problem: Which football player has greater momentum? Player A: mass = 60 kg; velocity = 2.5 m/s Player B: mass = 65 kg; velocity = 2.0 m/s | text | null |
L_0729 | newtons third law | T_3609 | When an action and reaction occur, momentum is transferred from one object to the other. However, the com- bined momentum of the objects remains the same. In other words, momentum is conserved. This is the law of conservation of momentum. Consider the example of a truck colliding with a car, which is illustrated in Figure 14.11. Both vehicles are moving in the same direction before and after the collision, but the truck is moving faster than the car before the collision occurs. During the collision, the truck transfers some of its momentum to the car. After the collision, the truck is moving slower and the car is moving faster than before the collision occurred. Nonetheless, their combined momentum is the same both before and after the collision. You can see an animation showing how momentum is conserved in a head-on collision at this URL: . | text | null |
L_0729 | newtons third law | T_3610 | Paul Doherty of the Exploratorium performs a "sit-down" lecture on one of Sir Issac Newtons most famous laws. For more information on Newtons laws of motion, see http://science.kqed.org/quest/video/quest-lab-newtons-laws- MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0729 | newtons third law | T_3611 | At UC Berkeley, a team of undergrads is experimenting with velocity, force, and aerodynamics. But you wont find them in a lab they work on a baseball diamond, throwing fast balls, sliders and curve balls. QUEST discovers how the principles of physics can make the difference between a strike and a home run. For more information on the physics of baseball, see http://science.kqed.org/quest/video/out-of-the-park-the-physics-of-baseball/ . MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0731 | buoyancy of fluids | T_3623 | Buoyancy is the ability of a fluid to exert an upward force on any object placed in the fluid. This upward force is called buoyant force. | text | null |
L_0731 | buoyancy of fluids | T_3624 | What explains buoyant force? Recall from the earlier lesson "Pressure of Fluids" that a fluid exerts pressure in all directions but the pressure is greater at greater depth. Therefore, the fluid below an object exerts greater force on the object than the fluid above the object. This is illustrated in Figure 15.12. Buoyant force explains why objects may float in water. No doubt youve noticed, however, that some objects do not float in water. If buoyant force applies to all objects in fluids, why do some objects sink instead of float? The answer has to do with their weight. | text | null |
L_0731 | buoyancy of fluids | T_3625 | Weight is a measure of the force of gravity pulling down on an object. Buoyant force pushes up on an object. Weight and buoyant force together determine whether an object sinks or floats. This is illustrated in Figure 15.13. If an objects weight is the same as the buoyant force acting on the object, then the object floats. This is the example on the left in Figure 15.13. If an objects weight is greater than the buoyant force acting on the object, then the object sinks. This is the example on the right in Figure 15.13. Because of buoyant force, objects seem lighter in water. You may have noticed this when you went swimming and could easily pick up a friend or sibling under the water. Some of the persons weight was countered by the buoyant force of the water. | text | null |
L_0731 | buoyancy of fluids | T_3626 | Density, or the amount of mass in a given volume, is also related to buoyancy. Thats because density affects weight. A given volume of a denser substance is heavier than the same volume of a less dense substance. For example, ice is less dense than liquid water. This explains why ice cubes float in a glass of water. This and other examples of density and buoyant force are illustrated in Figure 15.14 and in the video at this URL: MEDIA Click image to the left or use the URL below. URL: | text | null |
L_0731 | buoyancy of fluids | T_3627 | Did you ever notice that when you get into a bathtub of water the level of the water rises? More than 2200 years ago, a Greek mathematician named Archimedes noticed the same thing. He observed that both a body and the water in a tub cant occupy the same space at the same time. As a result, some of the water is displaced, or moved out of the way. How much water is displaced? Archimedes determined that the volume of displaced water equals the volume of the submerged object. So more water is displaced by a bigger body than a smaller one. What does displacement have to do with buoyant force? Everything! Archimedes discovered that the buoyant force acting on an object in a fluid equals the weight of the fluid displaced by the object. This is known as Archimedes law (or Archimedes Principle). Archimedes law explains why some objects float in fluids even though they are very heavy. Remember the oil tanker that opened this chapter? It is extremely heavy, yet it stays afloat. If a steel ball with the same weight as the ship were put into water, it would sink to the bottom (see Figure 15.15). Thats because the volume of water displaced by the steel ball weighs less than the ball. As a result, the buoyant force is not as great as the force of gravity acting on the ball. The design of the ships hull, on the other hand, causes it to displace much more water than the ball. In fact, the weight of the displaced water is greater than the weight of the ship, so the buoyant force is greater than the force of gravity acting on the ship. As a result, the ship floats. You can check your understanding of Archimedes law by doing the brainteaser at this URL: . For an entertaining video presentation of Archimedes law, go to this URL: http://videos.howstuffworks.com/disc | text | null |
L_0732 | work | T_3628 | Work is defined differently in physics than in everyday language. In physics, work means the use of force to move an object. The teen who is playing tennis in Figure 16.1 is using force to move her tennis racket, so she is doing work. The teen who is studying isnt moving anything, so she is not doing work. Not all force that is used to move an object does work. For work to be done, the force must be applied in the same direction that the object moves. If a force is applied in a different direction than the object moves, no work is done. Figure 16.2 illustrates this point. The stick person applies an upward force on the box when raising it from the ground to chest height. Work is done because the force is applied in the same direction as the box is moving. However, as the stick person walks from left to right while holding the box at chest height, no more work is done by the persons arms holding the box up. Thats because the force supporting the box acts in a different direction than the box is moving. A small amount of work in the horizontal direction is performed when the person is accelerating during the first step of the walk across the room. But other than that, there is no work, because there is no net force acting on the box horizontally. | text | null |
L_0732 | work | T_3629 | Work is directly related to both the force applied to an object and the distance the object moves. It can be represented by the equation: Work = Force Distance This equation shows that the greater the force that is used to move an object or the farther the object is moved, the more work that is done. You can see a short video introduction to work as the product of force and distance at this link: . To see the effects of force and distance on work, compare the weight lifters in Figure 16.3. The two weight lifters on the left are lifting the same amount of weight, but the bottom weight lifter is lifting the weight a longer distance. Therefore, this weight lifter is doing more work. The two weight lifters on the bottom right are both lifting the weight the same distance, but the weight lifter on the left is lifting a heavier weight. Therefore, this weight lifter is doing more work. | text | null |
L_0732 | work | T_3630 | The equation for work given above can be used to calculate the amount of work that is done if force and distance are known. For example, assume that one of the weight lifters in Figure 16.2 lifts a weight of 400 newtons over his head to a height of 2.2 meters off the ground. The amount of work he does is: Work = 400 N 2.2 m = 880 N m Notice that the unit for work is the newton meter. This is the SI unit for work, also called the joule (J). One joule equals the amount of work that is done when 1 newton of force moves an object over a distance of 1 meter. Problem Solving Problem: Todd pushed a 500 N box 4 meters across the floor. How much work did he do? Solution: Use the equation Work = Force Distance. Work = 500 N 4 m = 2000 N m, or 2000 J You Try It! Problem: Lara lifted a 100 N box 1.5 meters above the floor. How much work did she do? | text | null |
L_0732 | work | T_3631 | Did you ever rake leaves, like the woman in Figure 16.4? It can take a long time to do all that work. But if you use an electric leaf blower, like the man in the figure, the job gets done much sooner. Both the leaf blower and the rake do the work of removing leaves from the yard, but the leaf blower has more power. Thats why it can do the same amount of work in less time. | text | null |
L_0732 | work | T_3632 | Power is a measure of the amount of work that can be done in a given amount of time. Power can be represented by the equation: Power = Work Time In this equation, work is measured in joules and time is measured in seconds, so power is expressed in joules per second (J/s). This is the SI unit for work, also known as the watt (W). A watt equals 1 joule of work per second. The watt is named for James Watt, a Scottish inventor you will read about below. You may already be familiar with watts. Thats because light bulbs and small appliances such as hair dryers are labeled with the watts of power they provide. For example, the hair dryer in Figure 16.5 is labeled "2000 watts." This amount of power could also be expressed kilowatts. A kilowatt equals 1000 watts, so the 2000-watt hair dryer produces 2 kilowatts of power. Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. For example, compared with a low-power microwave, a high-power microwave can cook more food in the same time or the same amount of food in less time. | text | null |
L_0732 | work | T_3632 | Power is a measure of the amount of work that can be done in a given amount of time. Power can be represented by the equation: Power = Work Time In this equation, work is measured in joules and time is measured in seconds, so power is expressed in joules per second (J/s). This is the SI unit for work, also known as the watt (W). A watt equals 1 joule of work per second. The watt is named for James Watt, a Scottish inventor you will read about below. You may already be familiar with watts. Thats because light bulbs and small appliances such as hair dryers are labeled with the watts of power they provide. For example, the hair dryer in Figure 16.5 is labeled "2000 watts." This amount of power could also be expressed kilowatts. A kilowatt equals 1000 watts, so the 2000-watt hair dryer produces 2 kilowatts of power. Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. For example, compared with a low-power microwave, a high-power microwave can cook more food in the same time or the same amount of food in less time. | text | null |
L_0732 | work | T_3633 | Power can be calculated using the formula above, if the amount of work and time are known. For example, assume that a small engine does 3000 joules of work in 2 seconds. Then the power of the motor is: Power = 3000 J = 1500 J/s, or 1500 W 2s You can also calculate work if you know power and time by rewriting the power equation above as: Work = Power Time For example, if you use a 2000-watt hair dryer for 30 seconds, how much work is done? First express 2000 watts in J/s and then substitute this value for power in the work equation: Work = 2000 J/s 30 s = 60, 000 J For a video presentation on calculating power and work, go to this link: Problem Solving Problem: An electric mixer does 2500 joules of work in 5 seconds. What is its power? Solution: Use the equation: Power = Work Time . Power = 2500 J = 500 J/s, or 500 W 5s You Try It! Problem: How much work can be done in 30 seconds by a 1000-watt microwave? | text | null |
L_0732 | work | T_3634 | Sometimes power is measured in a unit called the horsepower. One horsepower is the amount of work a horse can do in 1 minute. It equals 745 watts of power. The horsepower was introduced by James Watt, who invented the first powerful steam engine in the 1770s. Watts steam engine led to a revolution in industry and agriculture because of its power. Watt wanted to impress people with the power of his steam engine, so he compared it with something familiar to people of his time: the power of workhorses, like those pictured in Figure 16.6. Watt said his steam engine could produce the power of 20 horses, or 20 horsepower. The most powerful engines today may produce more than 100,000 horsepower! How many watts of power is that? | text | null |
L_0733 | machines | T_3635 | A machine is any device that makes work easier by changing a force. When you use a machine, you apply force to the machine. This force is called the input force. The machine, in turn, applies force to an object. This force is called the output force. Recall that work equals force multiplied by distance: Work = Force Distance The force you apply to a machine is applied over a given distance, called the input distance. The force applied by the machine to the object is also applied over a distance, called the output distance. The output distance may or may not be the same as the input distance. Machines make work easier by increasing the amount of force that is applied, increasing the distance over which the force is applied, or changing the direction in which the force is applied. Contrary to popular belief, machines do not increase the amount of work that is done. They just change how the work is done. So if a machine increases the force applied, it must apply the force over a shorter distance. Similarly, if a machine increases the distance over which the force is applied, it must apply less force. | text | null |
L_0733 | machines | T_3636 | Examples of machines that increase force are doorknobs and nutcrackers. Figure 16.8 explains how these machines work. In each case, the force applied by the user is less than the force applied by the machine, but the machine applies the force over a shorter distance. | text | null |
L_0733 | machines | T_3637 | Examples of machines that increase the distance over which force is applied are paddles and hammers. Figure 16.9 explains how these machines work. In each case, the machine increases the distance over which the force is applied, but it reduces the strength of the applied force. | text | null |
L_0733 | machines | T_3638 | Some machines change the direction of the force applied by the user. They may or may not also change the strength of the force or the distance over which it is applied. Two examples of machines that work in this way are claw hammers and the rope systems (pulleys) that raise or lower flags on flagpoles. Figure 16.10 explains how these machines work. In each case, the direction of the force applied by the user is reversed by the machine. How does this make it easier to do the job? | text | null |
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