A child slides down a ball of ice.

[zaddyzad]

Homework Statement

Homework Equations

The Attempt at a Solution

 

[zaddyzad]

A and B are force and energy equations that may have some relevance. Bump.

 

[ehild]

How is Ek related to the mass m and speed v?

ehild

 

[billVancouver]

Hi zaddyzad,

I'm going to assume that the child was sitting on the top of the circle, initially at rest, though initial conditions aren't really clear from your attachment. Try these steps:

1. After sliding down to some angle theta, how far has the child fallen? Therefore, how much kinetic energy does the child have at that value of theta?

2. At that kinetic energy, how fast is the child moving? How much centripetal acceleration must be provided to keep the child moving in a circle at that velocity? How much centripetal force does this correspond to?

3. What is the component of gravity that points towards the center of the circle, when the child sits at angle theta? When does this equal the centripetal force needed from part 2?

Try to work through these steps yourself, and post what you get. We'll help you out if you get something wrong.

Hope this helps,
Bill Mills

 

[zaddyzad]

I think both my equations on the picture answers all the questions.

 

[Steely Dan]

Note that at the time when the normal force vanishes, you now have two equations with only two unknowns ($\theta$ and $v$). So you ought to be able to algebraically solve for both of those. See where that leads you.

 

[zaddyzad]

Though I actually have 3 variables because I don't know the radius.

 

[zaddyzad]

And the θ used in both equations is not the same number.