A factory worker pushes a 29.9 crate a distance of 4.0 along a level floor at co

Question

A factory worker pushes a 29.9 crate a distance of 4.0 along a level floor at constant velocity by pushing downward at an angle of 31 below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.24. Part A What magnitude of force must the worker apply to move the crate at constant velocity? Part B How much work is done on the crate by this force when the crate is pushed a distance of 4.0 ? Part C How much work is done on the crate by friction during this displacement? Part D How much work is done by the normal force? Part E How much work is done by gravity? Part F What is the total work done on the crate? PLEASE HELP ME ANSWER THESE QUESTIONS. THANK YOU.

Explanation / Answer

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

f = n = (m g + F sin31)

F cos31 = f = (m g + F sin31)

F * 0.857167 = 0.24 * (29.9*9.8 + F * 0.515038)

F = 0.24/0.857167 * (29.9*9.8) + F * (0.24*0.515038/0.857167)

F = 82.0433 + 0.144207 F

0.85579 F = 82.0433

F = 82.0433/0.85579

F = 95.868 N 95.9 N

Part B How much work is done on the crate by this force when the crate is pushed a distance of 4.0 ?

W = F d = 95.868 * 4.0 = 383 J

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

W = f d = F d = 383 J

Part D How much work is done by the normal force?

W = 0 J

Part E How much work is done by gravity?

W = 0 J

Part F What is the total work done on the crate?

W = 0 J

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