6.4 A factory worker pushes a 31.7kg crate a distance of 4.3m along a level floo

Question

6.4 A factory worker pushes a 31.7kg crate a distance of 4.3m along a level floor at constant velocity by pushing downward at an angle of 32? 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 4.3m ?

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

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

Part A)

The force must balance the frictional force.

F = uFn

Fn = (mg + Fsin32)

Fcos32 = u(mg + Fsin32)

.845F = (.26)(31.7)(9.8) + (.26)(.53)(F)

.710F = 80.77

F = 114 N

Part B)

W = Fd

W = (114)(4.3)

W = 489 J

Part C)

Frictional force acts opposite the direction of motion

Thus W = -489 J

Part D)

The normal force never does work since it acts perpendicular to the direction of motion.

W = 0 J

Part E)

The object is not moving up or down

Work by gravity is 0 J

Part F)

Total Work is 0 J

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