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# Seven Experiments on Gravity with your Smartphone (part 1)

Updated: Sep 13

Gravity, omnipresent in our everyday lives, remains a complex subject to grasp in its entirety. While Newton's portrayal of gravity as a force influencing all matter is widely recognized, it inevitably sparks a multitude of questions.

In our upcoming two-segment article, we outline seven intriguing experiments that can be conducted using just a smartphone to delve deeper into the realm of gravity. From embarking on a Zero G flight to exploring the behavior of a pendulum on the moon, venturing to the equator, or even attempting push-ups at 33,000 feet, we're set for a thrilling journey. Are you on board?

Table of content :

## What is gravity?

Gravity is a fundamental force in the universe that governs the interaction between bodies on a macroscopic scale. It is responsible for the mutual attraction between all objects possessing mass. When we drop an object, it falls towards the ground due to the gravitational force exerted by the Earth.

Galileo is the first to have studied in detail the phenomenon of gravity in a scientific way. Galileo's experiment on the fall of bodies from the top of the tower of Pisa is probably a myth, but many thought experiments that he conceptualized allowed him to show that, contrary to preconceived idea, two objects of different masses fall at the same speed. He also studied the mathematical rule that governs the distance travelled by a ball rolling freely along an inclined plane and found that it increases with the square of the time elapsed. Today we know that: d = 1/2*g*tÂ², where g is the acceleration of gravity.

This law will be demonstrated a century later with the theory of gravity proposed by Sir Isaac Newton. He postulates that every object in the universe attracts all other objects with a force proportional to their mass and inversely proportional to the square of the distance between them. According to Newton's law of universal gravitation, the gravitational force (F) between two objects of mass (m1) and (m2) separated by a distance (r) is given by the equation: F = G * (m1 * m2 ) / rÂ², where G is the universal gravitational constant, which has a value of approximately 6.674 Ã— 10^-11 N(m/kg)Â².

For an object on the surface of the earth, the gravitational force that applies to an object, also called the weight of the object, can be written simply: F = m * g, where g is the acceleration of the gravity, and m the mass of an object. The value of the acceleration due to gravity g is approximately 9.81 m/sÂ². The value of g, depends on a number of factors, like altitude or latitude (since the Earth is not a perfect sphere).

Newton's theory can explain many phenomena such as the movement of the planets. But it however fails to resolve some phenomenon like the gravitational lensing effet, or the precession of the orbit of Mercury. Also it does not explain where the gravitational force comes from and why its action is instantaneous. The theory of general relativity, formulated by Albert Einstein at the beginning of the 20th century, brings a revolutionary approach to gravity. Contrary to the Newtonian view of gravity as a force of attraction at a distance, Einstein describes gravity as a distortion of spacetime caused by the presence of mass and energy. In this theory, objects move along geodesic curves in curved spacetime, creating the effect perceived as a gravitational force. Thus, according to the theory of general relativity, gravity is not a mysterious force of attraction, but rather a consequence of the curvature of space-time induced by the distribution of mass and energy.

No that we know a bit more on gravity, let's experiment with it!

## Zero G flights

To train the astronauts in weightlessness, that is to say the absence of gravity, they are subjected to Zero G flights. The astronauts are placed in the empty cabin of the plane, the interior walls of the device are covered with mattresses. In these flights, the plane describes parabolas. During the end of the ascending phase, then the beginning of the descending phase, the astronauts can remove their safety belts and fly freely in the cabin as if they were weightless.

To better understand this phenomenon, let's do the following experiment. Let's put our smartphone on a table and then in FizziQ open the Absolute Acceleration measurement. We see the value of 9.81 m/sÂ² is displayed. Now let's orient the laptop differently in all directions. We will see that the value changes and then also stabilizes at the value 9.81 m/sÂ². This therefore means that the smartphone is subjected to a force equivalent to an acceleration of 9.81 m/sÂ². It is the acceleration of gravity. Yet the smartphone does not move, which means that the smartphone somehow measures the force created by the table in reaction to gravity.

Zero G - FizziQ

To prove this, le'ts remove the table. The smartphone falls, but what is the acceleration detected by the accelerometer ? We place a mattress on the floor, then press the Record button and we launch our smartphone so that it describes a parabola and falls on the mattress. Then Stop recording. We note that during the entire period in the air, the acceleration of the smartphone is zero. Although the smartphone was in free fall, and therefore its vertical speed varied for an observer placed on the ground, the accelerometer does not seem to perceive any movement, it acts as if the smartphone was in zero gravity.

Let's go back to the case of flight Zero G. At the beginning of the ascending phase, the astronauts are subjected to an acceleration which will cause them to describe a parabolic movement, then the plane slows down and aligns its vertical and horizontal speed with that of the passengers. The astronauts have the sensation of being weightless, as the cabin in which they are falls at the same speed as them. However, to an observer outside the plane, the astronauts would be in free fall.

The analysis of the Zero G flight can shed some light on what is happening to our smartphone and help us answer the question : why is acceleration null ? The accelerometer is a tiny electro-mechanical device made of a small weight connected to the frame by a spring. If the frame moves, the weight reacts with a delay and by measuring the change of distance between the frame and the weight, one can compute the acceleration of the frame (see our article on the subject). If we come back to our experiment, when the smartphone falls, all the parts of the smartphone fall together (the frame and the weight), and hence there is no relative movement of the weight versus the frame. As a consequence the measurer acceleration is zero. On the contrary when we hold the case, the weight is pulled down by gravity but the case is held fixed by our arm. So there is a relative move of one versus the other. The accelerometer then detects the reaction force of our arm, equal to gravity.

This experiment reminds Einstein's "elevator thought experiment" which was instrumental in developing the equivalence principle, central to his general theory of relativity. In the experiment, when inside a closed elevator in deep space that's accelerating upwards, a dropped ball appears to fall towards the floor similarly to Earth's gravitational pull. In contrast, a stationary elevator near a planet like Earth experiences a similar effect due to gravity. The essence of this thought experiment is that within the confines of the elevator, one cannot distinguish between effects of gravity and pure acceleration. The Zero G flight, an dour smartphone in free fall, are equivalent to elevators which fall with the same acceleration as gravity and hence give the impression of zero gravity.

## Let's estimate g!

One of the essential parameters of the theory of gravitation is the acceleration due to gravity, g. Depending on whether this value is high or low, we feel heavy like on Earth or light like on the Moon. We have seen that the accelerometer made it possible to estimate this value, but scientists in the 16th century did not have this instrument. Can we calculate g without using the accelerometer?

For this we are going to do the same experiment as Galileo and measure the time it takes for a body to fall from a certain height. We know that the relationship between the total duration t of the fall of an object and the height h at which this object is dropped is h = 1/2gtÂ². To calculate g we therefore only need to measure the duration of the fall of a given object from a known height.

Let's choose an object, for example a ball, and let's drop it from a certain height h, for example from the first floor of a building. With a smartphone stopwatch, we measure the duration of the fall. For example, by placing myself on the first floor of a building and dropping a ball, I obtained the value of 0.95 s of fall for 3.5 m, which gives a g value of 7.75 m/sÂ² .

This value is not very precise, because it is difficult to start and stop the timer at the exact moments when the ball is released and when it lands. This is because of this that Galileo used inclined ramps to conduct his analysis on falling balls, as they fall less quickly. An error of 10% on the duration results in an error of more than 20% on the measurement of g. Triggering the stopwatch by hand creates a lot of uncertainty, so we need to use a more precise method. In FizziQ we have the ability to record the sound volume over a given period. We will therefore create a device in which a sound is created when the object begins to fall and another when the object hits the ground. It will then not suffice for us to measure the time interval between these two events.

In this experiment, we drop a bolt from a shelf in such a way as to generate a noise when it begins its fall and another when it ends. Let's place the bolt at the very edge of the shelf then with a tool, we give a sharp blow to the bolt to push it into the void, creating a small characteristic noise.

Measuring gravity - FizziQ

When the bolt hits the ground, it makes another crash sound. With FizziQ we measure the time elapsed: we select the sound volume, then we start recording and we do the experiment described precisely. When the bolt hits the ground, we stop recording. By studying the data in the workbook, we can accurately determine the first and second shock, and therefore have an accurate measurement of the fall time.

The photo shows the device used and the graph, the measurement made. The floor has a height of 1.28 m and the measured duration is 0.51 s, which gives a value of g of 9.84 m/sÂ².

To improve the measurement, you can use a sound stopwatch as for the measurement of the speed of sound. You can also use a trigger with acceleration.

## A pendulum on the moon

In a NASA video taken during the Apollo14 mission on the surface of the Moon, we see that the period of a box that oscillates like a pendulum is significantly greater than that which this pendulum would have had on earth: https:// history.nasa.gov/alsj/a14/Apollo14SEQ_BayPendulum.mpg. Can we explain this phenomenon?

Galileo, the first to have carried out in-depth experiments on the movement of pendulums, he showed in 1632 that the period of the pendulum for weak oscillations does not depend on its mass, nor on the amplitude of the oscillations but only on its length. This remark will be the basis of clock movements that use pendulums. Huygens in 1659 determines the exact expression of the period of a pendulum for weak oscillations: T=2Ï€*âˆš(l/g), where g is gravity.

The period depends on the length l of the pendulum but also on a fundamental terrestrial parameter: the acceleration of gravity, g. This allowed scientists for the first time to accurately determine the constant g, or rather the length of a pendulum that had a period of one second. In 1690, in his Discourse on the cause of gravity, Huygens indicates that the length of the pendulum beating the second in Paris is 3 feet 8.66 lines or 0.9941 m, which corresponds to a gravity in Paris of 9.812 m/ sÂ² (with our units). The pendulum becomes at the time the instrument for measuring gravity.

We see that this formula the period is inversely proportional to the square root of g. On the moon, the period of a pendulum would therefore be 2.5 times greater than on the earth, verified by the calculations that scientists have made by analyzing the video of Apollo 14 and detailed on the NASA website: https: //history.nasa.gov/alsj/a14/a14pendulum.html.

As we are not on the Moon, we will check Galileo's formula on earth. We will use the luxmeter provided by the FizziQ application for smartphones to accurately calculate the period of a pendulum. We suspend a pendulum made with a fairly heavy ball at the end of a thread in such a way that the ball obscures the photoelectric cell of a smartphone when it is in the low position. The photocell of Android devices is usually placed to the right of the camera. It can be located by measuring the brightness with the FizziQ Illumination instrument and placing your finger where you think it is.

By measuring the illumination, we can very precisely determine the period of the pendulum which corresponds to the difference between two peaks of luminosity. We then verify Galileo's law on pendulums. We can also use this measurement to do more precise calculation of g.

## Trajectory of a fall

When watching a basketball game, we are used to seeing beautiful parabolas described by the balls when thrown from a distance. Can we model this curve? For this we use one of the most obvious assets of smartphones and tablets: the camera which allows the physicist to make precise videos of the movements he or she is studying. Thanks to the video analysis tools of the FizziQ application, you can also analyze in detail the kinematics of these movements, trace their trajectories and export the characteristics of the movements to a spreadsheet.

The user can either create his video of an object in free fall, or use one of the videos available in the application. The video library of the FizziQ application contains many videos, especially on sports, which can be used to study the kinematics of free fall: https://www.fizziq.org/cinematique.

For example, let's use the video of a bullet drop from the kinematics module. You can find in the following tutorial on Youtube how to conduct video analysis using FizziQ: https://www.youtube.com/watch?v=sZdndmHefH8.

Free fall - FizziQ

After having carried out the analysis of the fall, we place the data of the trajectory in the notebook of experiments. By plotting the graph for the vertical position of the ball as a function of time, we see that this trajectory is a parabola, thus confirming Galileo's result.

What is the equation of this parabola? By pressing down on the interpolation functions, we choose the quadratic interpolation which gives the equation of the trajectory. In graph 3, the equation of the interpolated function is f(x) = 4.72xÂ²-1.48x+2.05. This analysis also makes it possible to find the acceleration of weightlessness g = 2*4.72 = 9.44 m/sÂ².

Galileo's intuition on the dependence of the position of a falling ball on time was therefore correct!
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