Question

A box of mass M is pushed a distance L across a level floor by a constant applied force P. The coefficient of kinetic friction between the box and the floor is μ. Assuming the box starts from rest, express the final velocity vf of the box in terms of M, L, P, μ, and g.

Answer 1

Assuming the box starts from rest, the final velocity of the box in terms of M, L, P, μ, and g which is given as ::

From a free body diagram of mass, we have

F_x = P - f_s = m a                                      

where, f_s = static frictional force = _s N = _s m g

then   P - (_s m g) = m a

a = P - (_s m g) / m

using equation of motion 3,

v_f² = v₀² + 2 a L

where, v₀ = 0

v_f² = 2 [P - (_s m g) / m] L

v_f = 2 [P - (_s m g) / m] L