# Pulleys and rope problem

1. Jul 11, 2006

### Teegvin

Mass 1 = 10.0 kg
Mass 2 = 3.00 kg

The pulleys and rope are massless, and there is no friction.

What is the tension in the rope?

What is the acceleration of mass 1?

If my thinking is correct, the tension is half the weight of mass 2 (14.7 N), and the acceleration of mass 1 is 1.47 m/s^2.

My textbook gives the solutions as 13.7 N and 1.37 m/s^2.

Last edited: Jul 26, 2006
2. Jul 12, 2006

### Staff: Mentor

What makes you think that? Show your work and we can see what happened.

3. Jul 12, 2006

### BobG

You're right about the tension being evenly distributed on both sides of mass 2, but mass 2 isn't stationary. As mass 1 slides across the table, mass 2 is moving downward, so the net is less than weight of mass 2.

Try thinking about mass 1 first. The force required (10kg * a) equals the tension on either side of mass 2.

4. Jul 12, 2006

### Teegvin

I figured it out after I read this, and after I realised that the acceleration of mass 2 is half that of mass 1, because it goes half the distance in the same time.

m2(a1)/2 = m2g - 2T
= m2g - 2(10a1)
m2(a1)/2 + 20a1 = m2g
(3/2)a1 + 20a1 = 3g
(43/2)a1 = 3(9.80)
a1 = 1.37

Is this reasoning correct?

5. Jul 12, 2006

### Staff: Mentor

Looks good to me. (As a matter of style, I would solve for the acceleration in terms of m1 and m2. I wouldn't plug in the actual masses until the last step. But you've got it!)