Finding the Velocity of a Swinging Ball Around a Post

[jjd101]

Homework Statement

A ball on a 6.5 m long string swings down and wraps around a post that is 4.0 m below the post the string is attached to. If the ball is released level with the post to which it is attached, what will be the velocity of the ball when it is at its highest point over the lower post?

Homework Equations

circular momentum? Inertia of a ball on a string

The Attempt at a Solution

I really have no idea where to start on this problem, i was thinking you start with the initial acceleration of 9.8 due to gravity but that doesn't translate to an initial angular velocity.

 

[gneill]

Use conservation of energy! What forms of energy are involved here? Where's the energy coming from to give the ball motion?

 

[jjd101]

gravitiational potential energy and kinetic energy??

 

[gneill]

gravitiational potential energy and kinetic energy??

Yes. So determine the change in energies for the various locations.

 

[jjd101]

? do i split it up into sections like pie to 3pie/2, 3pie/2 to 2pie, 2pie to pie/2?

 

[gneill]

? do i split it up into sections like pie to 3pie/2, 3pie/2 to 2pie, 2pie to pie/2?

You can split it up any way you like, as long as you get the information you need in order to find the kinetic and potential energies at the various locations. Personally, since gravitational potential energy is involved, I'd be more concerned about the change in heights of the object at the various points, rather than any angle. Why not draw a picture of the situation at each critical point and see if you can label the changes in height.

 

[jjd101]

the change in height goes from 4m above the post to 2.5m above the post, aka 1.5m lesss than the drop point, but i don't know how to do this energy problem without mass?

 

[gneill]

the change in height goes from 4m above the post to 2.5m above the post, aka 1.5m lesss than the drop point, but i don't know how to do this energy problem without mass?

Leave it in as a variable if you wish; you'll find that it cancels out anyways.

 

[jjd101]

i left m in as a variable and ended up with velocity is equal to 5.42m/s. Is this correct?

 

[gneill]

i left m in as a variable and ended up with velocity is equal to 5.42m/s. Is this correct?

It looks fine.

 

[jjd101]

thanks