A 63.6-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.613 and 0.402, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?

a) 389.86 N

b) 255.67 N

Explanation:

a) When an object start to move the friction acting is static friction.

F = μ₁R = μ₁mg; R = mg, g = 10 m/s2

where, μ₁ = coefficients of static friction

R = normal reaction of flow

F = frictional force

F = 0.613*63.6*10 = 389.86 N

b) When an object is moving the friction acting is dynamic friction.

F = μ₂R = μ₂mg; g = 10 m/s2

where, μ₂ = coefficients of dynamic friction

F = 0.402*63.6*10 = 255.67 N