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 with this force unitil 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.

Answer 1

m = mass = 20 kg

us = cofficient of static friction = 0.2

uk = cofficient of kinetic friction = 0.1

R = normal reaction

F = applied force

f = friction force

b) from fig:

F = mg*sin40 + f

F = mg*sin40 + us*R

F = mg*sin40 + us*mg*cos40 [ R = mg*cos40]

F = 20*9.8*sin40 + 0.2*20*9.8*cos40

F = 156 N

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c) now crate is moving,So

F = mg*sin40 + uk*mg*cos40

= 20*9.8*sin40 + 0.1*20*9.8*cos40

= 141 N

F= ma

141 = 20*a

a ( acceleration) = 141/20 = 7.05 m/s²

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d) u = initial velocity = 0

V = final velocity = 1m/s

t = time= ?

V= u+a*t

1 = 0 + 7.05*t

t = 1/ 7.05

t = 0.1418 sec

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e) yes these answers pass through the common sense test.

in part b we have to calculate the force with which create will move,so we consider maximum friction force ie static friction force.

in part ca nd since create is moving so it will have accceleration and time.during motion friction force is kinetic friction.