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-qu

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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-qu

arter of a circle with radius 1.60 m (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 4.80 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.
A). What is the coefficient of kinetic friction on the horizontal surface?
b How much work is done on the package by friction as it slides down the circular arc from A to B ?

Physics

1 answer:

Murljashka [212] · Answer 1 · 2024-08-05T20:26:54+03:00

The coefficient of kinetic friction on the horizontal surface, μ = 0.39.

The work done on the package by friction as it slides down the circular arc from A to B, W = -4.176.

<h3>What is the frictional force acting on the package moving on the track?</h3>

Frictional force is the force which opposes the motion of an object over another.

Frictional force acts at the surface of contact of the objects.

The frictional force, F is related to the coefficient of kinetic friction on the horizontal surface, μ, and the normal reaction or weight, mg, of the package as follows:

F = μmg

Work done against friction, W = F * d

W = μmgd

The Kinetic energy of the package is equal to the work done against friction.

Kinetic energy of the package = mv²/2

μmgd = mv²/2

μ = v²/2gd

μ = 4.8²/(2 * 9.81 * 3)

μ = 0.39

b. Work done on the package by friction as it slides down the circular arc from A to B is given as follows:

W = mv²/2 - mgh

W = v²/2 - gh