A box Of textbooks of mass 25.9 kg rests on a load.ng ramp that makes an angle a

Question

A box Of textbooks of mass 25.9 kg rests on a load.ng ramp that makes an angle alpha with the horizontal. The coefficient of kinetic friction is 0.25 and the coefficient of static friction is 0 35. As the angle alpha is increased, find the minimum angle at which the box starts to slip. Express your answer using two significant figures. At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures. At this angle, how fast will the box be moving after it has slid a distance 5 1 m along the loading ramp? Express your answer using two significant figures

Explanation / Answer

part A)

If alfa is the minimum angle angle to slip on the ramp,

tan(alfa) = mue_s

alfa = tan^-1(mue_s)

= tan^-1(0.35)

= 19. degrees

B) apply net force acting on the box along the ramp,

Fnet = m*g*sin(19) - mue_k*N

m*a = m*g*sin(19) - mue_k*m*g*cos(19)

a = g*sin(19) - mue_k*g*cos(19)

= 9.8*sin(19) - 0.25*9.8*cos(19)

= 0.87 m/s^2

C) use, v^2 - u^2 = 2*a*d

v^2 - 0^2 = 2*a*d

==> v = sqrt(2*a*d)

= sqrt(2*0.874*5.1)

= 3.0 m/s

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