What are the tension and acceleration in this pulleys and rope problem?

[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.

 

[Doc Al]

If my thinking is correct, the tension is half the weight of mass 2...

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

 

[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.

 

[Teegvin]

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

I figured it out after I read this, and after I realized 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?

 

[Doc Al]

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!)