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 can be treated as a particle. It slides down the track and reaches point B with a speed v. From point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest. Find the velocity of the package at point B, assuming that there is no friction on the ramp. Find the coefficient of friction between the package at point B, assuming that there is no friction on the ramp. Find the coefficient of friction between the package and the horizontal surface.

Explanation / Answer

4.

a) for curved surface,

Applying energy conservation for position A to B;

KE + PE = constant

0 + m g R   = m v^2 /2 + 0

v = sqrt(2 gR) = sqrt(2 x9.8 x 1.60) = 5.6 m/s ..........Ans (Speed at B)

b) Now applying work- energy theorem,

Work done by friction = change in KE

friction force = f = uk mg

and work done by friction = - uk m g d

Applying:

- uk m g d = Kf - Ki = 0 - (m v^2 / 2 )

2 uk m g d = m v^2

uk = (5.6^2) / (2 x 9.8 x 3)

uk = 0.533

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