Question

A 20.0 kg mass is being pushed by a force of magnitude 20 N downwards from rest as shown in the Figure. Another mass of 24.0 kg is connected by a massless rope through a frictionless pulley. The coefficient of kinetic friction between the second block and the surface is 0.3.

What is the acceleration of the first block?
What is the tension on the rope?
How much distance does the 24 kg block cover in 3 seconds?

Answer 1

Point Y upward and X-axis to the right.

The 20-kg block is going down, the 24-kg block is moving to the left.

Apply Newton's first law for the pushed block:

$$Oy: -mg+T+F=-ma.$$

Apply the law for the block on the horizontal plane with friction:

$$Oy: -Mg=N,\\ Ox: -T+\mu N=-Ma,\\ -T+\mu Mg=-Ma.$$

Solve the system with T and a as unknown values:

$$a=\frac{g(m-\mu M)-F}{m+M}=2.4\text{ m/s}^2,\\\space\\ T=m(g-a)-F=128\text{ N}.$$

In 3 seconds from rest, the 24-kg block goes

$$d=\frac{at^2}{2}=10.8\text{ m}.$$