Circular Movement Homework: Part A Done, Part B Troubles

[asi123]

Homework Statement

Everything is in the pictures.
I did part A, I have a problem with part B.
10x in advance.

Homework Equations

The Attempt at a Solution

 

[Doc Al]

You need to find the tension as a function of angle. (Forget the tension at the top.)

You have the correct equation. Hint: Express v^2 as a function of angle.

 

[asi123]

You need to find the tension as a function of angle. (Forget the tension at the top.)

You have the correct equation. Hint: Express v^2 as a function of angle.

I know this equation (in the pic) but I'm doubtful if this what you meant...

Should I use trigo? can I get another tip ?

10x.

 

[Doc Al]

The equation I had in mind was: mv^2/r = T + mg cos(theta).

Another hint: What's conserved as the ball continues on its path?

 

[asi123]

The equation I had in mind was: mv^2/r = T + mg cos(theta).

Another hint: What's conserved as the ball continues on its path?

Ok, I already wrote that equation at the beginning in the solution part I uploaded and got stuck there.

I got stuck because I don't know the velocity at this point, I mean, the velocity is not constant, right? there is a mgsin(theta) that keep changing it...I think.

The velocity at the top is not the velocity at the bottom, right?

10x.

 

[Doc Al]

I got stuck because I don't know the velocity at this point, I mean, the velocity is not constant, right?

The velocity is definitely not constant. Reread my hint in post #4.

Given the velocity at the top, you should be able to find the velocity at any point as a function of angle.

 

[asi123]

The velocity is definitely not constant. Reread my hint in post #4.

Given the velocity at the top, you should be able to find the velocity at any point as a function of angle.

I'm totally stuck, should I use trigo, or there is some equation for the velocity that I don't know about...

Oh, maybe u mean to use energy calculation?

 

[Doc Al]

Oh, maybe u mean to use energy calculation?

Getting warmer!

 

[asi123]

Getting warmer!

The potential energy turns into kinetic energy, no?

 

[Doc Al]

You got it. Keep going.

 

[asi123]

Ok, I haven't really learned Conservation of energy so I'm not really familiar with it...

I wrote this equation about the energy, is it correct?

And another thing, What about T? it's not a Conservative force, right? Do I just ignore it in the the energy equation?

10x.

 

[Doc Al]

Ok, I haven't really learned Conservation of energy so I'm not really familiar with it...

I wrote this equation about the energy, is it correct?

Looks good to me.

And another thing, What about T? it's not a Conservative force, right? Do I just ignore it in the the energy equation?

Excellent question! Ask yourself: Does the tension force do any work on the ball?

 

[asi123]

Looks good to me.

Excellent question! Ask yourself: Does the tension force do any work on the ball?

Oh, right, it's vertical to his movement.

10x a lot.

 

[Doc Al]

The ball's movement is always perpendicular to the tension, thus the tension does no work on the ball.