Conservation of Energy and Centripital Motion question

[ubermuchlove]

Homework Statement

A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down the side. At what point does she lose contact with the snowball and fly off tangent? That is, at the instant she loses contact with the snowball, what angle alpha does a radial line from the center of the snowball to the skier make with the vertical?

Homework Equations

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The Attempt at a Solution

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[jimmyting]

I will help you to start, use energy conservation from the top of the snowball to the point (with angle alpha) where she loses contact. Try that and if you have any more questions, just ask

 

[ubermuchlove]

let h1= top of the snowball and h2= the height at which she loses contact

K1 + U1 = K2 + U2
0 + mgh1 = mgh2 + 1/2mv^2
gh1 = gh2 + 1/2v^2
g(h1-h2)= 1/2v^2
v^2/R (h1-h2) = 1/2v^2
h1-h2=R/2
h2= h1-R/2

this is as far as i got. h2 is the point at which the skier looses contact.

 

[jimmyting]

good but notice what you are solving for. How do you bring alpha into this. Hopefully you already drew a diagram, so substitute alpha and h1 in for h2.

 

[tiny-tim]

At what point does she lose contact with the snowball and fly off tangent?

Hi ubermuchlove!

This is a forces question … like a rollercoaster …

Calculate the normal force, N.

She will lose contact when N is zero!

 

[ubermuchlove]

yes, but i am still clueless as to how to incorporate alpha.
im honestly missing something big here?

 

[tiny-tim]

yes, but i am still clueless as to how to incorporate alpha.

Hint: what are the forces? when you calculate the forces, something is going to be multiplied by either cosα or sinα.