Work Energy: Find Tension at Bottom of Circle

[hsphysics2]

Homework Statement

A 1.3kg stone is whirled in a vertical circle at the end of a 0.83m long string. The tension in the string at the top of the circle is 6.4N. What is the tension in the string when the stone is at the bottom of the circle?

Homework Equations

F_c= ma_c
W=|F||Δd|cosθ

W_ALL= E₂- E₁

E= 1/2 mv²- mgh

The Attempt at a Solution

I think I'd have to find the speed of the stone at the bottom of the circle first but I'm not sure how to start it.

 

[Andrew Mason]

Homework Statement

A 1.3kg stone is whirled in a vertical circle at the end of a 0.83m long string. The tension in the string at the top of the circle is 6.4N. What is the tension in the string when the stone is at the bottom of the circle?

Homework Equations

F_c= ma_c
W=|F||Δd|cosθ

W_ALL= E₂- E₁

E= 1/2 mv²- mgh

The Attempt at a Solution

I think I'd have to find the speed of the stone at the bottom of the circle first but I'm not sure how to start it.

Draw a free-body diagram of the stone at the top of the circle and at the bottom.

Can you calculate the difference in the (centripetal) acceleration from the change in kinetic energy? How does that difference in centripetal acceleration relate to the difference in tension?

AM

 

[haruspex]

I think I'd have to find the speed of the stone at the bottom of the circle first but I'm not sure how to start it.

If the speed at the top is u and the speed at the bottom is v, what equations can you write relating u to v, u to the tension at the top, and v to the tension at the bottom?

 

[cepheid]

I think the sequence of steps would go something like this:

- figure out the net force on the stone at the top of the circle. This is the centripetal force.
- based on this centripetal force, what must be the speed at the top?
- from conservation of energy, if that was the speed at the top, what will be the speed at the bottom?
- based on this speed at the bottom, what centripetal force is required, and therefore how much tension (keeping in mind that at the bottom, the stone's weight hinders, rather than helps, the centripetal force).

 

[Andrew Mason]

I think the sequence of steps would go something like this:

- figure out the net force on the stone at the top of the circle. This is the centripetal force.
- based on this centripetal force, what must be the speed at the top?
- from conservation of energy, if that was the speed at the top, what will be the speed at the bottom?
- based on this speed at the bottom, what centripetal force is required, and therefore how much tension (keeping in mind that at the bottom, the stone's weight hinders, rather than helps, the centripetal force).

In this problem you do not have to find the speed at the top (although you can do that). You just need to know the difference in kinetic energy between top and bottom.

AM