Forces- two pulleys w. diff accelerations

[Maiia]

Homework Statement

In the drawing the rope and the pulleys are massless and frictionless, and there is no friction between the table and the block. Find the tension in the rope and the acceleration of the 10kg block.

Here is my drawing of the problem and my FBDs and equations.

I assumed that if the acceleration of the 10kg block was "L," the acceleration of the 3kg block would be 1/2 L because it is split between the two tensions...?

I would appreciate it if someone could check my work for this problem because I don't seem to be getting the right answer...

 

[alphysicist]

Hi Maiia,

Homework Statement

In the drawing the rope and the pulleys are massless and frictionless, and there is no friction between the table and the block. Find the tension in the rope and the acceleration of the 10kg block.

Here is my drawing of the problem and my FBDs and equations.


I assumed that if the acceleration of the 10kg block was "L," the acceleration of the 3kg block would be 1/2 L because it is split between the two tensions...?

I would appreciate it if someone could check my work for this problem because I don't seem to be getting the right answer...

In your equation for the 3kg mass, you have:

$$2T - F_g = \frac{3}{2} L$$
where L is the acceleration of the 10kg block. You seem to have a sign error here. Remember that everything with the same sign is going in the same direction, which would mean that this equation is saying the acceleration of the 3kg mass is in the same direction as the tension (and in the opposite direction of the force of gravity).