How far does this block move?

Question

Here’s my question I’m working on:

A 30.0kg block sits on a plane inclined at 25.0° to the horizontal, and is attached by means of a cord and pulley to a 20.0 kg mass that hangs freely. If the 20.0kg mass is allowed to fall, determine how far it’ll move in 2.00s, starting from rest. Neglect any friction.

I think we’re supposed to calculate velocity which is initially 0m/s because the block is at rest. however the 20.0kg mass is confusing me because that’ll increase the acceleration going down.

Answer 1

There are two forces acting on the block. One is a force acting to accelerate the block down the slide given by 30 kg x 9.8 m/s² x sin 25. The other is a retarding force from the hanging 20 kg block (20 kg x 9.8 m/s²). The net force is the sliding force minus the force from the hanging block. The net force can be equated to 30 kg x a and solved for a to get the actual acceleration down the slide. Finally, the distance traveled in two seconds an be obtained by the formula S = 1/2 x a x t²) where a is the calculated acceleration and t is 2 seconds. The result is in meters. Draw a diagram showing the forces acting on the block to help visualize the problem.