# Circular motion and work done by non conservative forces

## 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.

Orodruin
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There is no non-conservative force in this problem. As stated explicitly:
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.

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?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
2021 Award
No, you would have to account for the additional work done on the system.

• Maged Saeed
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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