# Work and Energy with Tension

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1. Jul 15, 2016

### Auburn2017

1. The problem statement, all variables and given/known data
Refer to figure.

2. Relevant equations
U=Fs
T=.5mv^2
Vg=mgh

3. The attempt at a solution
I am not exactly sure where to start. I would appreciate if someone could nudge me in the right direction and then go from there.

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2. Jul 15, 2016

### haruspex

Start with a free body diagram of the mass when theta is 180. Write out the ΣF=ma equation for it.

3. Jul 15, 2016

### Auburn2017

I have done that but I am not sure how to get the velocity of the mass...

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4. Jul 15, 2016

### haruspex

Your diagram seems to be for theta = 90 degrees.

For the velocity, any conservation law come to mind?
(In your 'relevant equations', I don't understand Vg=mgh. What is Vg there?)

5. Jul 15, 2016

### Auburn2017

yeah my figure is incorrect. Vg is the gravitational potential energy

6. Jul 15, 2016

### haruspex

Ok. I thought it more usual to use E or U for energy. What is the T in the preceding equation? Well, I can guess from the equation what it is, but why 'T'?

7. Jul 15, 2016

### Auburn2017

kinetic energy. it's just the notation we use.

8. Jul 15, 2016

### haruspex

Ok, so what relates that to Vg?

9. Jul 15, 2016

### Auburn2017

U=ΔT-ΔV where V=Vg+Ve and Ve is the elastic potential energy(spring) but it isn't applicable to this problem

10. Jul 15, 2016

### haruspex

Let's investigate that. No spring here, so Ve is zero. What is U? Can you assign a value to it?

11. Jul 15, 2016

### Auburn2017

U=ΔE=(T2-T1)+(VG2-VG1)

12. Jul 15, 2016

### billy_joule

That's right.
What is the value of ΔE? In other words, does any energy enter or exit the system? (you are expected to assume the nudge does not add any kinetic energy to the pendulum).

13. Jul 17, 2016

### Auburn2017

There are no external forces so now work is done on the system causing E=0. I figured out how to work in on my own. Thank you for your reply.