Conservation of Energy and Centripital Motion question

AI Thread Summary
The discussion focuses on a physics problem involving a skier descending a frictionless snowball and determining the angle at which she loses contact with the surface. Participants suggest using conservation of energy to relate the skier's height and speed at the point of losing contact. The key point is that the normal force becomes zero at the moment of losing contact, which is crucial for solving the problem. To incorporate the angle alpha, it's important to analyze the forces acting on the skier, specifically using trigonometric functions like sine and cosine. The conversation emphasizes the need for a clear understanding of the forces involved to find the solution.
ubermuchlove
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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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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
 
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.
 
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.
 
ubermuchlove said:
At what point does she lose contact with the snowball and fly off tangent?

Hi ubermuchlove! :smile:

This is a forces question … like a rollercoaster …

Calculate the normal force, N.

She will lose contact when N is zero! :smile:
 
yes, but i am still clueless as to how to incorporate alpha.
im honestly missing something big here?
 
ubermuchlove said:
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. :smile:
 
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