Circular motion and work done by non conservative forces

This is a basic principle of conservation of energy. Therefore, if there are no non-conservative forces, there would be no loss in mechanical energy.
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Homework Statement


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 T⃗t and T⃗b. T⃗t and T⃗b have magnitudes Tt and Tb.

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

Homework Equations


Ki+Ui+WNC = Kf+Uf

The Attempt at a Solution


Ki+WNC = Kf+Uf
WNC = Kf+Uf - Ki
WNC = (1/2)mvt2 + mg2L - (1/2)mvb2


Top:
Tt = (mvt2/L) - mg
Bottom:
Tb = mg - (mvb2/L)

I don't know what to do after this. I have work done by non conservative forces, but I'm not sure how to relate this to the difference in tensions.
 
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  • #2
There is no non-conservative force in this problem. As stated explicitly:
henry3369 said:
Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy.

You should be able to use conservation of total energy (including the gravitational potential energy) in order to relate the velocities, and thus also the tensions.
 
  • #3
Orodruin said:
There is no non-conservative force in this problem. As stated explicitly:


You should be able to use conservation of total energy (including the gravitational potential energy) in order to relate the velocities, and thus also the tensions.
Oh okay. I got the answer when the work done by non-conservative force = 0. If the problem didn't explicitly state that no mechanical energy is lost, could you still assume that WNC = 0?
 
  • #4
No, you would have to account for the additional work done on the system.
 
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  • #5
henry3369 said:
If the problem didn't explicitly state that no mechanical energy is lost, could you still assume that WNC = 0?
Yes, Because the loss in mechanical energy is equal to the work done by the non-conservative forces in an isolated systems
 
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