Posted by John Miller on Monday, April 8, 2013 at 9:23pm.
A box of books weighing 314 N is shoved across the floor by a force of 475 N exerted downward at an angle of 35° below the horizontal.
(a) If μk between the box and the floor is 0.53, how long does it take to move the box 5.00 m starting from rest?
What is the maximum coefficient of kinetic friction between the box and the floor that allows the box to move from this applied force.

physics  Henry, Tuesday, April 9, 2013 at 10:16pm
Wb = 314 N.
m*g = 314
m = 314/g = 314/9.8=32 kg.=mass of box.
Fb = 314N[0o].
Fp = 314*sin(0) = 0 = Force parallel to floor.
Fv = 314*cos(0)+475*sin35 = 586 N. =
Force perpendicular to floor.
Fk = u*Fv = 0.53 * 586 = 310.6 N. = Force of kinetic friction.
a. Fap*cos35FpFk = m*a
475*cos350310.6 = 32*a
389310.6 = 32a
78.4 = 32a
a = 2.45m/s^2.
d = 0.5a*t^2 = 5 m.
0.5*2.45t^2 = 5
1.225t^2 = 5
t^2 = 4.082
t = 2.02 s.