Q4) A ball of mass m is attached to a string of length L . It is being swung in

Question

Q4) A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion.(Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T? t and T? b. T? t and T? b have magnitudes Tt and Tb.

http://session.masteringphysics.com/problemAsset/1011022/22/MPE_ug_1_001.jpg

Find Tb?Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle.

Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer.

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Q5) 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 4.10m/s . From point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest.

http://session.masteringphysics.com/problemAsset/1260249/2/YF-07-39.jpg

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?

A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion.(Figure 1) Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T? t and T? b. T? t and T? b have magnitudes Tt and Tb. Find Tb?Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle. Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer. 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 4.10m/s. From point B, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest. What is the coefficient of kinetic friction on the horizontal surface? How much work is done on the package by friction as it slides down the circular arc from A to B?

Explanation / Answer

1)T(b)-mg=m*v(b)^2 / L..........(1)

T(t)+mg=m*v(t)^2 / L.............(2)

by conservation of energy

1/2mv(b)^2=1/2mv(t)^2+2mgL

v(b)^2-v(t)^2=4gL

subtract (1),(2)

t(b)-t(t)=2mg+m/L ( v(b)^2-v(t)^2)

=2mg+m/L*4gL

=2mg+4mg

=6mg

2)

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*4.1*4.1/3) = 0.56 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*4.1*4.1) = 1.455 J

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