How Is a Skier's Gravitational Potential Energy Affected by a Mountain Lift?

In summary, the conversation discusses a 70 kg skier riding a 2700 m long lift to the top of a mountain at an angle of 14.3°. The question asks for the change in the skier's gravitational potential energy, for which the correct formula is mgh, where h is the change in height. The formula (h0 - hf) * cos(?) is incorrect. By using trigonometry, the correct change in height is found to be 2700*sin14.3. Plugging this value into the formula mgh, the final result is 4.6E-5, which is correct.
  • #1
rcmango
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0

Homework Statement



A 70.0 kg skier rides a 2700 m long lift to the top of a mountain. The lift makes an angle of 14.3° with the horizontal. What is the change in the skier's gravitational potential energy?

Homework Equations





The Attempt at a Solution



mg cos(?) * (h0 - hf)


again, not sure why this formula doesnot work.
 
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  • #2
The GPE near the Earth's surface is mgh where h is the height above some reference height.

Thus a change in GPE is mgΔh where Δh is the change in height.

In your equation (h0 - hf) looks like a change in height -- which is what you want, so why should it be multipled by cos(?)?
 
  • #3
Using trig. you can find that (hf - ho ) = 2700*sin14.3. Using this value you can find gravitational potential energy.
 
  • #4
okay so gpe = m * g * (chng in height)

so this is what i get 70 * 9.8 * (667.)

and get something like: 4.6E-5

okay, that's correct. thanks alot.
 
  • #5
A 70.0 kg skier rides a 2700 m long lift to the top of a mountain. Can you explain this sentence? Which is his starting point? "2700m long lift" Is it the distasance between the starting point and the end point?
 

FAQ: How Is a Skier's Gravitational Potential Energy Affected by a Mountain Lift?

What is skier's gravitational energy?

Skier's gravitational energy is the potential energy that a skier possesses due to their position and height above the ground. It is a form of stored energy that can be converted into kinetic energy as the skier moves downhill.

How is skier's gravitational energy calculated?

The calculation of skier's gravitational energy involves multiplying the mass of the skier by the acceleration due to gravity (9.8 m/s^2) and the height of the skier above the ground. The formula is E = mgh, where E is the gravitational energy, m is the mass, g is the acceleration due to gravity, and h is the height.

Does the speed of a skier affect their gravitational energy?

Yes, the speed of a skier does affect their gravitational energy. As the skier moves faster downhill, their potential energy decreases and their kinetic energy increases. This means that their gravitational energy is converted into kinetic energy, making them move faster.

Can skier's gravitational energy be increased or decreased?

Yes, skier's gravitational energy can be increased or decreased depending on their position. If they move higher up on a slope, their gravitational energy will increase. If they move closer to the ground, their gravitational energy will decrease.

How is skier's gravitational energy relevant to skiing?

Skier's gravitational energy is relevant to skiing because it is the energy that allows them to move downhill and perform jumps and tricks. As they ski down a slope, their gravitational energy is converted into kinetic energy, which propels them forward. Understanding this energy can also help skiers make strategic decisions on where to ski and how to control their speed.

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