A box of textbooks of mass 24.4 kg rests on a loading ramp that makes an angle x

Question

A box of textbooks of mass 24.4 kg rests on a loading ramp that makes an angle x with the horizontal. The coefficient of kinetic friction is 0.230 and the coefficient of static friction is 0.350.

* As the angle x is increased, find the minimum angle at which the box starts to slip.

* At this angle, find the acceleration once the box has begun to move. Take the free fall acceleration to be g= 9.80 m/s^2 .

* At this angle, how fast will the box be moving after it has slid a distance 5.50 m along the loading ramp? Take the free fall acceleration to be g= 9.80 m/s^2 .

Explanation / Answer

1)normal force=mgcosx
for box to start to slip---- (static) * normal = mgsinx

so (static)mgcosx=mgsinx

tanx=(static)

x=19.29 degree angle.

2)when the box begin to move,kinetic friction will owrk

so a=gsinx-(kinetic)gcosx

=(static)gcosx-(kinetic)gcosx

a=0.113g[g=9.8]

3)v=(2a*s)=(2*0.113*9.8*5.5)=3.49m/s

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