Acrate with mass m = 4.25 kg rests on the top of a counter. the coefficient of static friction between the crate and the counter is μs = 0.62 and the coefficient of kinetic friction is μk = 0.47.
(a) write an expression for fm the minimum force required to produce movement of the book on the top of the bar.
(b) solve numerically for the magnitude of the force fm in newtons.

Explanation:

Given

mass of crate

coefficient of static friction

coefficient of kinetic friction

For movement of book we need to provide a force which can overcome the static friction i.e.

where N=normal Reaction

and Normal reaction is equal to the weight of body

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s