Question

An inclined plane making an angle of 25o with the horizontal has a pulley at the top. A 30kg block on the plane is connected to a freely hanging 20kg block by means of a cord passing over the pulley. Compute the distance the 20kg block will fall in 2 seconds starting from rest. Neglect friction.

Answer 1

This is the diagram of setup which I made by question statement

let m1 = 30 kg

m2 = 20 kg

The 30 kg mass will have m1gsin25 acting parallel to the plane and m1gcos25 acting perpendicular to the plane.

so,

Using Newton's second law, we have

F_net = ma

m2g - m1gsin25 = ( m1 + m2)a

a = m2g - m1gsin25 / m1 + m2

a = 20 * 9.8 - 30 * 9.8 * sin 25 / 20 + 30

a = 1.435 m/s²

we have got the acceleration of the system, now we can easily find the distance for 20 kg block

using kinematics, assuming the 20 kg block starts from rest

h = ut + 1/2at²

here u = 0

so,

h = 1/2at²

h = 1/2 * 1.435 * 2²

h = 2.87 m