you are moving a 50 kg crate by sliding it. you push on the crate with a force of 315 n at 21 degrees below the horizontal. the coefficient of kinetic friction is 0.21. how far does the crate move in 15 seconds?

Answer 1

force down on ground = 50*9.81+315sin 21
so
friction force = .21(50*9.81+315sin 21)
so in the horizontal direction
F=ma= 50 a = 315cos21 -.21(50*9.81+315sin 21)
solve for a
I assume that the initial speed is zero
then
x = (1/2)a t^2 = 112.5 * a

Answer 2

M*g = 50 * 9.8 = 490 N. = Wt. of the crate.

Fn = 490*Cos 0 + 315*sin21 = 602.9 N. = Normal force.

Fk = u*Fn = 0.21 * 602.9 = 126.6 N. = Force of kinetic friction.

Fap-Fk = M*a.
315*Cos21-126.6 = 50a, a = ?.

d = 0.5a*t^2, t = 15s.