Question

A mover tries to push a crate up a straight ramp that makes an incline with the horizontal of 40 degrees. Assume the force of the man's push is parallel to the ramp surface. The mass of the crate is 20 kg. The coefficient of static friction of the crate with the ground is 0.2 and the coefficient of kinetic friction is 0.1.

a) Draw a sketch of the situation and a force diagram of the crate, labeling all forces clearly.

b) With what force does the man have to push to start the crate moving from rest?

c) If he continues to push with this force after the crate is moving, what will be its acceleration?

d) How long will he have to push the with this force unitil the it is moving at 1 m/s?

e) Discuss whether or not your answers to parts b through d pass the "common sense" test -do not discuss your method. Be specific about why you think the answers do or do not make sense. For example, explain how the force you calculate compares to the force required to pick up the crate directly.

Answer 1

b] The upward force [along the ramp] must be atleast equal to the sum of downwards force [component along the downward direction of slope] of gravity and the frictional force.

=>

c] After the crate starts to move, the frictional force will be kinetic in nature and so the net force will be:

=>

And by Newton's 2nd Law, F_net = ma

so, a = 15.01/20 = 0.751 m/s².

d]

u = 0 m/s

v = 1 m/s and a = 0.751 m/s²

use, v = u + at

so, 1 = 0 + 0.751t

=> t = 1.33s.