A crate of 50.9-kg tools rests on a horizontal floor You exert a gradually incre

Question

A crate of 50.9-kg tools rests on a horizontal floor You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 329 N. After that you must reduce your push to 204 N to keep it moving at a steady 23.5 cm/s What is the coefficient of static friction between the crate and the floor? What is the coefficient of kinetic friction between the crate and the floor? What push must you exert to give it an acceleration of 1.23 m/s^2 ? Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62 in/s^2. What magnitude push would cause it to move? What would its acceleration be if you maintained the push in part C?

Explanation / Answer

Net force on the crate = Your force – Friction force = mass * acceleration
Fr = µ * m * g
The mass of the crate = 50.9 Kg
Fr = µ * 50.9 * 9.81
F – µ * 50.9 * 9.81 = 50.9 * a

The 329 N force is used to determine the coefficient of static friction. The 204 N force is used to determine the coefficient of kinetic friction. In both situations, the acceleration is 0 m/s^2
F = µ * 50.9 * 9.81

Part A what is the coefficient of static friction between the crate and the floor?
329 = µ * 50.9 * 9.81 =======> µ = 0.66

Part B
What is the coefficient of kinetic friction between the crate and the floor?
204 = µ * 50.9 * 9.8 =======> µ = 0.409

Part C
What push must you exert to give it an acceleration of 1.23 ?
Since the crate is moving, use the coefficient of kinetic friction.
F – µ * 50.9 * 9.81 = 50.9 * 1.23

Part D
Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62 . What magnitude push would cause it to move?
Replace 9.81 with 1.62 and use the coefficient of static friction.

Part E
What would its acceleration be if you maintained the push in part C?
Replace 9.81 with 1.62 and use the coefficient of kinetic friction.

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