How Does Tension Affect Energy Conservation in a Pendulum System?

[Auburn2017]

Homework Statement

Refer to figure.

Homework Equations

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

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.

 

[haruspex]

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

 

[Auburn2017]

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

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

 

[haruspex]

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

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?)

 

[Auburn2017]

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?)

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

 

[haruspex]

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

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'?

 

[Auburn2017]

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'?

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

 

[haruspex]

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

Ok, so what relates that to Vg?

 

[Auburn2017]

Ok, so what relates that to Vg?

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

 

[haruspex]

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

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

 

[Auburn2017]

U=ΔE=(T₂-T₁)+(V_G2-V_G1)

 

[billy_joule]

U=ΔE=(T₂-T₁)+(V_G2-V_G1)

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).

 

[Auburn2017]

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).

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.