Relating tensions in a vertical circle help

[samjohnny]

Homework Statement

Question: A mass m attached to a light string is spinning in a vertical circle, keeping its total energy constant. Find the difference in the magnitude of the tension between the top most and bottom most points.

The Attempt at a Solution

So for this one I've worked out that the tension at the top=(mVt^2/r)-mg and at the bottom=(mVb^2/r)+mg where r=radius of circle, Vb is the velocity at bottom and Vt is velocity at top. And I've also worked out that, since the total energy is conserved, Energy at top [KE+PE]=Energy at bottom [KE+PE] ==> [(mVt^2)/2]+mg2r=(mVb^2)/2.

But I don't where to go from there and work out the two tensions. Any suggestions?

Thanks

 

[TSny]

Hello.

You don't need to work out the tensions individually. You just need to find the difference in the tensions. Find an expression for the difference in tensions and then invoke your energy relation to simplify the expression for the difference.

 

[samjohnny]

Hello.

You don't need to work out the tensions individually. You just need to find the difference in the tensions. Find an expression for the difference in tensions and then invoke your energy relation to simplify the expression for the difference.

Thanks for the reply. Ok, if I'm understanding you correctly, would I equate the forces with Newton's second and obtain two vector equations for the two tensions? In which case, how would I take into account the energy?

 

[TSny]

In your first post, you gave expressions for the tension at the bottom, T_b, and the tension at the top,T_t. Use those to get an expression for the difference T_b - T_t.

 

[samjohnny]

In your first post, you gave expressions for the tension at the bottom, T_b, and the tension at the top,T_t. Use those to get an expression for the difference T_b - T_t.

Ah yes, thanks a lot I've got it now. :)