The man pushes on the 60lb crate with a force F The force is

The man pushes on the 60-lb crate with a force F. The force is always directed down at 30 degree from the horizontal as shown, and its magnitude is increased until the crate begins to slide. Determine the crate\'s initial acceleration if the coefficient of static friction is mu_s= 0.6 and the coefficient of kinetic friction is mu_k = 0.3.

Solution

Fx and Fy are components of weight, Fg; FN is normal force; Ff is friction

Since Ff = 0, and FN is cancelled by Fy, Fx is the net force

Fnet = Fx

ma = mgsinø

a = gsinø [eqn 1]

a.

a = gsinø

ø = sin -1( .6 / 3.0) = 11.3º

a =(9.8)sin11.3º = 1.92 m/s2

Applying vf2 = vi2+ 2ad gives

vf2 = 0 + 2(1.92)(3.0)

vf = 3.40 m/s