Question

A box of textbooks of mass 25.0 kg rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.24 and the coefficient of static friction is 0.37.

FIND
A) As the angle α is increased, find the minimum angle at which the box starts to slip.

B)At this angle, find the magnitude of the acceleration once the box has begun to move.

C)At this angle, how fast will the box be moving after it has slid a distance 4.8 m along the loading ramp?

Answer 1

M*g = 25 * 9.8 = 245 N.

Fp = 245*sinA.

Fn = 245*CosA.
Fs = u*Fn = 0.37 * 245*CosA = 90.7*CosA. = Force of static friction.
Fki = u*Fn = 0.24*245*CosA = 58.8*CosA. = Force of kinetic friction.

A. Fp-Fs = M*a.
245*sinA-90.7*CosA = 25*0.
245*sinA/CosA-90.7 = 0,
245*TanA = 90.7,
TanA = 90.7/245,
A = 20.3 Degrees.

B. Fp-Fki = M*a.
245*sin20,3-58.8*Cos20,3 = 25a,
25a = 29.9,
a = 1.2 m/s^2.

C. V^2 = Vo^2 + 2a*d = 0 + 2.4*4.8 = 11.52,
V = 3.4 m/s.