# If two books are tied together with a string

1. Aug 19, 2013

### UnD3R0aTh

1. If two books are tied together with string and one is pushed off the edge of a table. What the acceleration of the two books?

Zero
g/2
g
a value between zero and g
a value that could be greater than g

2. gravity acceleration laws

3. G, because gravity acceleration is independent of mass

2. Aug 19, 2013

### sjb-2812

What are your thoughts? Why for instance should the acceleration be higher, or lower, or the same?

3. Aug 19, 2013

### UnD3R0aTh

my thoughts are posted above lol

4. Aug 19, 2013

### voko

Are you familiar withe Newton's second law?

Let the book on the table have mass m. The book hanging on the string has mass M.

What forces act on the books?

What are their accelerations (use Newton's second law here)?

5. Aug 19, 2013

### UnD3R0aTh

two forces gravity downwards, and the tension of the thread which is equal to the weight of the other book plus friction upwards

6. Aug 19, 2013

### voko

Friction? What friction? Do you even have to consider friction here? Read your problem carefully.

What about accelerations? What about Newton's second law?

7. Aug 19, 2013

### UnD3R0aTh

ok no friction, when one book is pushed off the table it falls with force equal to it's weight according to newton's second law, it's accelerated with the gravity acceleration which is equal to 9.8 m/s2, the book will free fall with that acceleration until it pull the other book, at which point the other book will slow down the first book initially but both will start accelerating with G again, all objects fall down with G regardless of their mass so it's got to be G, your opinion?

8. Aug 19, 2013

### voko

No, this is not what Newton's second law states.

There are three phases here, you are quite correct. First is when the one book is falling freely, and the string is not taut.

Second is when the string is taut, and one book is falling - not freely! - and the other is sliding over the table.

Third is when both books are falling freely.

You have the correct answers for the first and the third phases. The answer for the second phase ("slow down") is also correct, but could be expanded.

9. Aug 19, 2013

### UnD3R0aTh

newton's second law is f = mg force or weight is equal mass times acceleration, so what would be the accurate answer for the middle phase?

10. Aug 19, 2013

### voko

Newton's second law is ma = F, where a is acceleration (not necessarily the free fall acceleration), and F is the sum of all forces (not necessarily just the weight).
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