A box of textbooks of mass 25.9 rests on a loading ramp that makes an angle with

Question

A box of textbooks of mass 25.9 rests on a loading ramp that makes an angle with the horizontal. The coefficient of kinetic friction is 0.25 and the coefficient of static friction is 0.37. a)As the angle is increased, find the minimum angle at which the box starts to slip. B)At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures. c)At this angle, how fast will the box be moving after it has slid a distance 5.0 along the loading ramp? Express your answer using two significant figures C)

Explanation / Answer

a)Force down the ramp = mgsinA
Force up the ramp =mgcosA (static friction coefficient)

mgsin(A) -mgcos(A) = 0
tan(A) =
tan(A) = 0.37
A = 20.3 0

b)Once it starts moving, we use the kinetic friction coefficient.

ma = mgsin(A) -mgcos(A) (down the ramp)
a = gsin(A) - gcos(A)
= g(sin(A) - cos(A))
= 9.80 m/s^2*(sin(20.3) - 0.250*cos(20.3))
= 3.15m/s^2

C)v^2 = v0^2 + 2ax
v0=0
v^2 = 2ax = 2*(3.15 m/s^2)*(5m)
v = 31.5 m/s

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