Solving the Physics of a Skier Leaving a Hill

To solve this problem, you can use the conservation of energy and the balancing of forces. The skier starts from rest, so the initial kinetic energy is zero. At the top of the hill, the skier has potential energy due to their height above the ground. As they slide down the hill, their potential energy is converted into kinetic energy. When the skier reaches a certain distance below the top of the hill, their potential energy will be completely converted into kinetic energy. At this point, the skier will become airborne because the normal force from the hill will become zero. Using the equation for centripetal force, you can show that the skier will become airborne at a distance of h=R/3 below the top of the hill
  • #1
austindubose
17
0

Homework Statement


A skier starts from rest at the top of a large hemispherical hill. Neglect friction and show that the skier will leave the hill becoming airborne at a distance of h=R/3 below the top of the hill. R is the radius of the hemispherical hill.


Homework Equations


Conservation of energy, balancing of forces, centripetal force = m(v2/r)


The Attempt at a Solution


I know this has to do with when the normal force becomes zero (or at least that's what I think). But I have no idea how to start this; can anyone point me in the right direction?
 
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  • #2
You are on the right track.
 

1. How does the angle of the slope affect a skier leaving a hill?

The angle of the slope plays a crucial role in determining the acceleration and speed of the skier leaving the hill. A steeper slope will result in a faster acceleration and higher speeds, while a flatter slope will result in a slower acceleration and lower speeds.

2. What is the impact of the skier's mass on their descent from a hill?

The skier's mass affects their descent from a hill in terms of their velocity and momentum. A heavier skier will have a greater momentum and will require more force to slow down or stop, while a lighter skier will have less momentum and will require less force to change their speed or direction.

3. How does friction factor into a skier's descent from a hill?

Friction between the skis and the snow can either help or hinder a skier's descent from a hill. In some cases, friction can provide the necessary grip and control for the skier to navigate the slope safely. However, too much friction can slow the skier down and make it more difficult to maintain their speed and direction.

4. What role does air resistance play in a skier's descent from a hill?

Air resistance, also known as drag, can affect a skier's descent from a hill by slowing them down. The faster the skier's speed, the more air resistance they will experience, which can make it more difficult for them to maintain their velocity. Skiers can minimize air resistance by keeping their body in an aerodynamic position.

5. How can a skier use their body position to control their descent from a hill?

A skier's body position can greatly impact their descent from a hill. By shifting their weight and center of mass, a skier can control their speed, direction, and balance. For example, leaning forward can increase speed and make turns sharper, while leaning back can slow them down and provide more stability. Additionally, keeping the body low and close to the ground can help reduce air resistance and improve overall control.

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