Conservation of Energy and Centripital Motion question

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Homework Help Overview

The problem involves a skier descending a frictionless snowball and seeks to determine the angle at which she loses contact with the snowball as she moves tangentially. The context is rooted in the principles of conservation of energy and forces in circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using energy conservation to relate the skier's height and speed at the point of losing contact. There are attempts to express the height in terms of the angle alpha and the radius of the snowball. Questions arise regarding how to incorporate the angle alpha into the equations and the forces acting on the skier.

Discussion Status

Some participants have provided guidance on using energy conservation and the concept of normal force to approach the problem. There is an ongoing exploration of how to relate the angle alpha to the forces involved, with multiple interpretations being considered.

Contextual Notes

Participants express uncertainty about incorporating the angle alpha into their calculations and mention the need for diagrams to visualize the problem. There is an acknowledgment of the forces acting on the skier at the point of losing contact.

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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