Problem 7.65 In a truck-loading station at a post office, a small 0.200-kg packa
ID: 1311864 • Letter: P
Question
Problem 7.65
In a truck-loading station at a post office, a small 0.200-kg package 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 Bwith a speed of 5.00m/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
Kientic energy of the package at B = 1/2mv^2.
It is lost in doing work against frictional force F = F*s = 3F
F = 0.5mv^2/ 3 = (0.5*0.2*5*5/3) = 0.834 N
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2.
P,E at the top mgh
This is used up in giving k.e to the package and work against friction.
Work against friction = mgh - 0.5mv^2
h = radius of the path.
(0.2*9.8*1.6) - (0.5*0.2*5*5) = 0.636 J
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