Question

A crate of 41.3-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 337 N . After that you must reduce your push to 202 N to keep it moving at a steady 20.0 cm/s .

Part A.) What is the coefficient of static friction between the crate and the floor? (static fraction=???)

Part B.) What is the coefficient of kinetic friction between the crate and the floor? (kinetic friction=??)

Part C.) What push must you exert to give it an acceleration of 1.44 m/s2 ? (F=???N)

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 m/s2. What magnitude push would cause it to move? (F=?? N)

Part E.) What would its acceleration be if you maintained the push in part C? (a=?? m/s^2)

Answer 1

(PART A)
Let the coefficient of static Friction = us
Force needed to start moving crate = us *N
337 N = us * m*g

us = 337/ (41.3 * 9.8)
us = 0.83  
Coefficient of static friction between the crate and the floor, us = 0.83

(PART B)
Let the coefficient of Kinetic Friction = uk
Force needed to move with constant velocity = 202 N

F - uk *N = 0
uk * mg = F
uk = 202/ (41.3 *9.8)
uk = 0.5
Coefficient of Kinetic Friction, uk = 0.5

(PART C)
We know , Force = m*a
F - uk*N = m*a
F = ma + uk * mg
F = 41.3 (1.44 + 0.5*9.8) N
F = 261.8 N
Force to be given, F = 261.8 N

(PART D)
Magnitude of Push needed on Moon = Fm
Assuming Coefficient of Friction is same that we calculated above.

Fm = us*mg
Fm = 0.83 * 41.3 * 1.6
Fm = 54.85 N
Magnitude of Push needed on Moon , Fm = 54.85 N