Acceleration along a pulley with a ledge

[fontseeker]

Homework Statement

Homework Equations

F = ma

The Attempt at a Solution

The solution to the problem is 1.12m/s^2. However, I don't know how they got to that number. Every way I do it I end up with 3.2m/s^2.

 

[Doc Al]

Hint: Do the masses have the same acceleration?

 

[fontseeker]

Hint: Do the masses have the same acceleration?

They do, so that is why I am treating acceleration with the same variable for both. The answer book says they have the same acceleration but in different direction, but the magnitude should be the same.

 

[Doc Al]

They do, so that is why I am treating acceleration with the same variable for both. The answer book says they have the same acceleration but in different direction, but the magnitude should be the same.

Rethink that. If the 20 kg mass moves 1 m to the right, how far does the other mass move down? (Consider the string.)

 

[fontseeker]

Rethink that. If the 20 kg mass moves 1 m to the right, how far does the other mass move down? (Consider the string.)

0.5m down. However, that means that they are both positive then? However, I don't know how to prove it, it just makes sense since the tension is twice as much on the 20kg object.

 

[Doc Al]

0.5m down.

No. If the 20 kg mass moves 1 m to the right, how much rope must have passed over the pulley?

 

[fontseeker]

No. If the 20 kg mass moves 1 m to the right, how much rope must have passed over the pulley?

One meter would have had to pass.

 

[Doc Al]

One meter would have had to pass.

Nope. Draw yourself a quick picture of before and after and measure the length of the string that must have passed. (Or grab an actual piece of string and try it.)

 

[fontseeker]

Nope. Draw yourself a quick picture of before and after and measure the length of the string that must have passed. (Or grab an actual piece of string and try it.)

Ah okay, since it is moving to the right 1 meter, 1 meter at the top and 1 meter at the bottom are loose, meaning 2 meters down.

 

[Doc Al]

Ah okay, since it is moving to the right 1 meter, 1 meter at the top and 1 meter at the bottom are loose, meaning 2 meters down.

Good! So how must the accelerations of the two masses relate to each other?

 

[fontseeker]

Good! So how must the accelerations of the two masses relate to each other?

The acceleration of the second block would be twice the acceleration of the first.

 

[Doc Al]

The acceleration of the second block would be twice the acceleration of the first.

Exactly. Now rewrite your equations with that in mind.

 

[fontseeker]

Exactly. Now rewrite your equations with that in mind.

I get 2.45m/s^2, which is the answer I see all over the internet. However, on my book this is what it says:

 

[Doc Al]

I get 2.45m/s^2, which is the answer I see all over the internet.

That's the correct answer for the acceleration of the 20 kg mass.

However, on my book this is what it says:

That answer makes no sense for this problem. What book is this?

 

[fontseeker]

That's the correct answer for the acceleration of the 20 kg mass. That answer makes no sense for this problem. What book is this?

Tipler

 

[Doc Al]

Tipler

I have the 6th edition, which has that as problem 4-81. The answers seem OK to me.

 

[Doc Al]

(That answer in your book must be a typo or something.)