A factory worker pushes a 29.1 kg crate a distance of 4.9 m along a level floor

Question

A factory worker pushes a 29.1 kg crate a distance of 4.9 m along a level floor at constant velocity by pushing downward at an angle of 32degrees below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.24. Express answers using two sig figs

Part:

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 4.9 m ?

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

A) Let F is minimum applied force is needed.

When, Fnetx = 0, the crate moves with constant speed.

F*cos(32) - mue_k*N = 0

F*cos(32) - mue_k*(m*g + F*sin(32)) = 0

F*(cos(32 - mue_k*sin(32)) = mue_k*m*g

F = mue_k*m*g/(cos(32) - mu_k*sin(32))

= 0.24*29.1*9.8/(cos(32) - 0.24*sin(32))

= 95 N

B) W(applied force) = F*d*cos(32)

= 95*4.9*cos(32)

= 395 J

C) Workdone by friction = -395 J

D) Workdone by normal force = 0

E) Workdone by gravity = 0

F) Total Workdone = 0

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