Conservation of Energy and Centripital Motion question

Click For Summary
SUMMARY

The discussion focuses on a physics problem involving a skier descending a frictionless snowball and determining the angle alpha at which she loses contact with the snowball. The conservation of energy principle is applied, leading to the equation g(h1 - h2) = 1/2v^2, where h1 is the initial height and h2 is the height at which contact is lost. The normal force, N, is crucial in this scenario, as the skier loses contact when N equals zero. Participants emphasize the need to incorporate angle alpha into the calculations to solve for the exact point of contact loss.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with forces and motion, particularly normal force calculations
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Ability to analyze motion in a circular path
NEXT STEPS
  • Study the application of conservation of energy in circular motion scenarios
  • Learn how to calculate normal force in various contexts
  • Explore the relationship between angle and forces in circular motion
  • Investigate the dynamics of objects losing contact with curved surfaces
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of energy conservation and forces in circular motion.

ubermuchlove
Messages
7
Reaction score
0

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


-_-


The Attempt at a Solution


-_-
 
Physics news on Phys.org
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:
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
5K
  • · Replies 12 ·
Replies
12
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
2K
  • · Replies 29 ·
Replies
29
Views
1K
  • · Replies 8 ·
Replies
8
Views
16K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 4 ·
Replies
4
Views
3K