Determine the smallest possible speed of the bob at A

[Alexanddros81]

Homework Statement

14.34 The 0.5-kg bob of the pendulum travels a complete circle about the pivot
point O. Determine the smallest possible speed of the bob in position A if it is
suspended from (a) a rigid rod of negligible mass; and (b) a string

Homework Equations

The Attempt at a Solution

[/B]
I can see that the above solution is not correct.
Do I take the potential energy at A to be 0 and potential energy at $B=mgy$ where y = 4 ?

Can you check this?

Any hints for part (b)?

 

[scottdave]

It looks like you swapped the kinetic energies of A and B. You have T_A + V_A on left side of one line, then it goes to 0 - 2mg on the left side of the next line. T_A is -2mg, but V_A should be ½mv², and V_B should be 0.

Taking point A to be y=0 is a valid strategy, as well.

 

[Alexanddros81]

Ah yes you're right about the swapped kinetic energies. I wasn't consentrated.
Here is the corrected solution:

Is this correct?
Any hints for part (b)?

 

[BvU]

Any hints for part (b)?

What's the critical point in the trajectory in case of a string ?

 

[haruspex]

Any hints for part (b)?

What is the essential difference between a rod and a string, both being massless?

 

[Alexanddros81]

Hi! I have found this:
https://physics.stackexchange.com/q...on-in-string-and-light-rod-in-vertical-circle

A movement of a string pendulum above 90deg will cause the string to fold up.
However, this does not happen if the pendulum bob is moving fast enough and its speed v never reaches zero when it goes up
above 90deg Then the pendulum swings in a full circle and keeps going in the same direction into the next circle.

How do interpret this to equation form?

 

[BvU]

For the rod u_B=0 was the limiting case because the rod could take the weight of the bob.
For the string the bob has to pull on it in order to keep it stretched. The limiting case is when the tension in the string reaches zero. What determines the tension in the string at various positions ?