In a truck-loading station at a post office, a small 0.200-kgpackage is released

Question

In a truck-loading station at a post office, a small 0.200-kgpackage is released from rest at point A on a track that is one-quarter of a circle with radius 1.60 m (the figure (Figure 1) ). The size of the package is much less than 1.60 m, so the package can be treated as a particle. It slides down the track and reaches point B with a speed of 4.00 m/s . From point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest.

Part A

What is the coefficient of kinetic friction on the horizontal surface?

Part B

How much work is done on the package by friction as it slides down the circular arc from A to B?

Explanation / Answer

W from B to C=Ec-Eb

=1/2mvc^2+mghc-(1/2mvb^2+mghb)

-umg(Xa-xb)=0+0-1/2mvb^2-0

rearranging we get

u=1/2(vb^2/2g(xa-xb)

=0.5*4^2/2*9.8(3-1.6)

u=0.29--answer a

b)WA to B=Eb-Ea

=1/2mvb^2 +mghb-1/2mva^2-mgha

=1/2*(0.200)(4)^2-(0.200)*9.8*1.60

=-1.36J--answer b

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