Conservation of energy of a skier

In summary, the skier will experience the same change in gravitational potential energy on all runs, as the height is the same. The speed at the bottom will also be the same for all runs. However, the skier will reach the bottom the quickest on the steepest path due to the influence of the slope on the vertical acceleration. The force of gravity on a slope with an incline will be less than the force of gravity on a vertical drop, as it is multiplied by the cosine of the angle of the slope.
  • #1
brycenrg
95
2

Homework Statement


A skier starts at the top of a friction less hill. You have 4 different runs, they have different difficulties. So I am assuming they are at different inclines. 1) longest route, not so steep 2) medium length, little steeper 3) shorter more steep 4) straight path, and very steep 5) all the same

On which run does her gravitational potential energy change the most?

On which run would her speed at the bottom be the fastest?

Which run would she get to the bottom the the quickest?

Homework Equations


Ei = Ef
mgh = 1/2mv^2

The Attempt at a Solution


Since Potential Energy = mgh
H is the same, I can assume. P converts into K
mgh = 1/2mv^2
so the final velocity will be the same for all. Kinetic energy is not a vector quantity either.
The gravitational potential energy will change the same amount in all runs.
The speed will be the same at the bottom for all runs.
She would get to the bottom the quickest at the steepest path. but would still have the same final energy or velocity/KE at the bottom.

Is this correct? for the longest time i thought they would get to the bottom at the same time but i don't think so anymore.
[/B]
 
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  • #2
brycenrg said:

Homework Statement


A skier starts at the top of a friction less hill. You have 4 different runs, they have different difficulties. So I am assuming they are at different inclines. 1) longest route, not so steep 2) medium length, little steeper 3) shorter more steep 4) straight path, and very steep 5) all the same

On which run does her gravitational potential energy change the most?

On which run would her speed at the bottom be the fastest?

Which run would she get to the bottom the the quickest?

Homework Equations


Ei = Ef
mgh = 1/2mv^2

The Attempt at a Solution


Since Potential Energy = mgh
H is the same, I can assume. P converts into K
mgh = 1/2mv^2
so the final velocity will be the same for all. Kinetic energy is not a vector quantity either.
The gravitational potential energy will change the same amount in all runs.
The speed will be the same at the bottom for all runs.[/B]


Correct so far...

brycenrg said:
She would get to the bottom the quickest at the steepest path. but would still have the same final energy or velocity/KE at the bottom.

Is this correct? for the longest time i thought they would get to the bottom at the same time but i don't think so anymore.

What does your last sentence mean?

The motion of the skier can be thought as the resultant of its vertical motion and its horizontal motion. The vertical displacement h is the same for all routes. The displacement is h = a/2 t2. How does the vertical acceleration depend on the steepness of the slope?
 
  • #3
What does your last sentence mean?

The motion of the skier can be thought as the resultant of its vertical motion and its horizontal motion. The vertical displacement h is the same for all routes. The displacement is h = a/2 t2. How does the vertical acceleration depend on the steepness of the slope?[/QUOTE]

If I fell off of a height of H. The force of gravity is mg
Now if I fell off a slope with 80 decline. The force of gravity is only mg(cos(10)). Is this correct way in thinking?
 

Related to Conservation of energy of a skier

What is conservation of energy and how does it apply to a skier?

Conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the context of a skier, this means that the total amount of energy (kinetic and potential) present in the system remains constant, regardless of any changes in speed or height.

What are the different forms of energy involved in skiing?

In skiing, there are two main forms of energy involved: potential energy, which is the energy associated with an object's position or height, and kinetic energy, which is the energy associated with an object's motion. These energies can be converted into each other as the skier moves down the slope.

How does a skier conserve energy while skiing?

A skier conserves energy by efficiently transferring potential energy into kinetic energy as they move downhill. This means choosing a smooth and efficient path down the slope, minimizing any wasted movements or resistance, and maintaining a constant speed with minimal braking or stopping.

What factors affect the conservation of energy for a skier?

Several factors can affect the conservation of energy for a skier, including the steepness of the slope, the skier's body position and technique, the type of snow and surface conditions, and the equipment used. Wind resistance and friction can also play a role in energy conservation.

How does the conservation of energy impact a skier's performance?

The conservation of energy is crucial for a skier's performance as it allows them to maintain a consistent and efficient speed throughout their run. By minimizing the loss of energy due to friction or inefficient movements, a skier can conserve energy and improve their overall performance on the slopes.

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