# Double pulley problem-difference in acceleration

1. Sep 22, 2011

### Arait

Double pulley problem--difference in acceleration

1. The problem statement, all variables and given/known data

http://img339.imageshack.us/img339/8793/picture1jv.png [Broken]

2. Relevant equations

a= g(M-m)/M+m

3. The attempt at a solution

Okay, so overall, pulleys just confuse me. We barely mentioned them in class and there's precious little about them in our books. I tried to answer this question and was able to get the first part (a) by finding the above equation on Google. However, as the question would lead you to assume, the answer to be is NOT the same. The problem is, I see no difference other than the fact that a box was replaced by hand. I don't understand why, if the downward force is the same, you would get a different acceleration. Because I don't understand this, it's making it pretty much impossible to know what to change in order to solve part b. I don't even know where to get started...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 5, 2017
2. Sep 22, 2011

### Staff: Mentor

Re: Double pulley problem--difference in acceleration

You should learn how this formula was derived using Newton's 2nd law.

To see the difference between the two situations, compare the tension in the rope. Are they the same? Is the tension in version a equal to the weight of the second mass?

3. Sep 22, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I'm still lost. The mass of the hand is probably different from the mass of the block, but as long as the force is the same, I don't see how it would change anything.

4. Sep 22, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I found something in my book that says that a the force T applied at one end of amassless rope is transmitted undiminished to the other end. Does this mean that T=958 N on both sides?

5. Sep 23, 2011

### Staff: Mentor

Re: Double pulley problem--difference in acceleration

True, if the force were the same then there would be no difference in the two scenarios. But is the force the same?

Answer my question: Is the tension in version a equal to the weight of the second mass?

6. Sep 23, 2011

### Staff: Mentor

Re: Double pulley problem--difference in acceleration

Yes, for a massless rope the tension is the same throughout.
What makes you think that that's the tension?

7. Sep 23, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I don't know. It's the opposite of gravity? I know that doesn't work since there's acceleration other than gravity acting in the downward direction, but I don't know how to solve for tension when there are so many variables you don't know.

8. Sep 23, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I'm betting it's not... But I don't know how to calculate it.

9. Sep 23, 2011

### Staff: Mentor

Re: Double pulley problem--difference in acceleration

You can solve for the tension and the acceleration--which are the only two unknowns in case a--by applying Newton's 2nd law to each mass. Start by identifying the forces on each.

(In case b you are given the tension, so it should be easier to calculate the acceleration.)

10. Sep 23, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I got it right by taking 958-(small mass)(g)=(small mass)(a). I got a=12.99 m/s^2. So, my homework is now done, but even though I figured out the right number, I'm still conceptually having a problem seeing the difference between Case A and Case B.

11. Sep 23, 2011

### Staff: Mentor

Re: Double pulley problem--difference in acceleration

That's not quite correct. Is it reasonable that the acceleration of the masses would be greater that something in free fall?

Show how you arrived at this result.
You'll need to redo your solution for case a. Then you can compare the tension in each case. (What's the tension in case b?)

12. Sep 23, 2011

### Arait

Re: Double pulley problem--difference in acceleration

I think I kinda see it now. Thanks!