Rectilinear Kinetics Example

A 200-lb block rests on a horizontal surface. What force P is required

to cause a horizontal acceleration of 10 ft/s2. The kinetic coefficient of

friction between the floor and the block is: mk = 0.25

Ff = N mk

S Fx = m ax

P cos 30 - Ff = ma

P cos 30 - N mk = ma (eqn. 1)

S Fy = m ay = 0

N - W - P sin 30 = 0

N = 200 + P sin 30 (eqn. 2)

Substitute eqn. 2 into eqn. 1

P cos 30 - (200 + P sin 30) mk = ma

a = 10 ft/s2, m = 200 lb/ (32.2 ft/s2)

solving, P = 151.3 lb