A factory worker pushes a 28.9 kg crate a distance of 4.0 m along a level floor

Question

A factory worker pushes a 28.9 kg crate a distance of 4.0 m along a level floor at constant velocity by pushing downward at an angle of 28 below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.26.

a)

What magnitude of force must the worker apply to move the crate at constant velocity?

b)

How much work is done on the crate by this force when the crate is pushed a distance of 4.0 m ? Express your answer using two significant figures.

c)

How much work is done on the crate by friction during this displacement?

Express your answer using two significant figures.

d) How much work is done by the normal force?

e) How much work is done by gravity?

f) What is the total work done on the crate?

Explanation / Answer

If F= force applied by the worker

then Fx cos 28 will act in forward direction and F xsin 28 will act towards downward.

so, total downward force= weight of crate + F x sin 28

= 28.9 x 9.8 + F x sin 28

= 283.22 + F sin 28

so normal force = total downward force

= 283.22 + F sin 28

so frictional force = coefficient of kinetic friction between the crate and floor x normal force

=0.26 x ( 283.22 + F sin 28)

but as the crate moves with a constant speed,

frictional force = F xcos 28 ( force acting in forward direction)

so,0.26 x ( 283.22 + F sin 28)= F xcos 28

so, F= 96.77 N

the worker must apply 96.77 N

b.

work done by this force = F x d x cos28

= 96.77 x cos 28 x 4

= 341.8 j

c.

work done by friction = friction force x displacement x cos 180

=96.77 x cos 28 x 4

=-341.8 j

d.

work done by normal force =0

as angle between normal force and displacement is 90 degree and

work done = force x displacement x cos 90 where cos90=0

e.

work done by gravity =0

as angle between force of gravity and displacement is 90 degree

work done = force x displacement x cos 90 where cos90=0

f.

total work done on the crate= work done by force + work done by friction + work done by normal force + work done by gravity

= 341.8 -341.8+0+0=0

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