Problem 7.65 In a truck-loading station at a post office, a small 0.200- surface
ID: 1396273 • Letter: P
Question
Problem 7.65 In a truck-loading station at a post office, a small 0.200- surface? kg package is released from rest at point A on a track that is one-quarter of a circle with radius 1.60 in (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 4.90 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
a) Work done = change in energy
let WBC = work done by friction force from B to C ( W= -f*d, f = u*N, N = mg)
= - u*mg*d ( W= - u*mg*d)
WBC = K.Ec - K.EB
- u* mg*d = (1/2)*m*Vc2 - (1/2)*m*VB2 ( Vc = 0 due to at rest)
- u*mg*d = 0- ( 1/2)*m*VB2
u = VB2 / 2*g*d
u = 4.902 / 2*9.8*3
u = 0.408
b) let WAB = work done from A to B
WAB = energy at B - energy at A
= ( 1/2)* m*VB2 - (1/2)*m*VA2 - mgh
= ( 1/2)*m*VB2 - 0 - mgh ( VA = 0 due to at rest)
= (1/2)* 0.200*4.902 - 0.200*9.8*1.60
= - 0.735 J