In a truck-loading station at a post office, a small 0.200-kg package is release

Question

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) The size of the package is much less than 1.60 m, so the package cna be treated as a particle. It slides down the track and reaches point B with a speed is Form point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest. (a) Find the velocity of the Package at point B, assuming that there is no friction on the ramp. (b) Find the coefficient of friction between the package and the horizontal surface.

Explanation / Answer

a)
between point A and B since there is no frictional force, use conservation of energy
use:
m*g*h = 0.5*m*v^2
g*h = 0.5*v^2
9.81*1.60 = 0.5*v^2
v = 5.6 m/s
Answer: 5.6 m/s

b)
From B to C , all kinetic energy is lost against friction
0.5*m*v^2 = frictional force*d
0.5*m*v^2 = miu*m*g*d
0.5*v^2 = miu*g*d
0.5*5.6^2 = miu*9.81*3
miu = 0.53
Answer: 0.53

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