Conservation of Energy ski-jump ramp

In summary, the skier's mechanical energy in the initial and final states were equal, with the initial energy being 691.16 J and the final energy being 288 J. The difference of 403.16 J represents the amount of mechanical energy lost due to air drag. However, this calculation does not account for the work done by air resistance.
  • #1
lauriecherie
44
0

Homework Statement



A 79 kg skier leaves the end of a ski-jump ramp with a velocity of 26 m/s directed 25° above the horizontal. Suppose that as a result of air drag the skier returns to the ground with a speed of 24 m/s, landing 18 m vertically below the end of the ramp. From the launch to the return to the ground, by how much is the mechanical energy of the skier-Earth system reduced because of air drag?



Homework Equations



Total Mechanical Energy initial = Total Mechanical Energy final where Total mechanical energry is all energies added.



The Attempt at a Solution



I took gravitational potential energy initial to be mgh and added that with kinetic energy initial, which is .5*m*velocity initial ^2. I set all this equal to the same thing, but as the finals of each of these energies. Then I saw that the difference between the two is 403.16. This seems like an awful lot. The answer should be in joules. Is my answer correct?
 
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  • #2
It will be more Joules than that right?

How many Joules in gravitational potential alone? And it ends with less velocity?
 
  • #3
LowlyPion said:
It will be more Joules than that right?

How many Joules in gravitational potential alone? And it ends with less velocity?

I got 691.16 J for the total mechanical energy initial. For the total mechanical energy final I came out with 288 J. So it was reduced by 288 J?
 
  • #4
lauriecherie said:
I got 691.16 J for the total mechanical energy initial. For the total mechanical energy final I came out with 288 J. So it was reduced by 288 J?

1/2*mv2 initial = 691 J ?

Can you show your calculation?

Isn't it 1/2 * 79 * 262 ?
 
  • #5
LowlyPion said:
1/2*mv2 initial = 691 J ?

Can you show your calculation?

Isn't it 1/2 * 79 * 262 ?

I added the Kinetic energy plus the gravitational potential energy initial. I then set that equal to total mechanical energy final which only included kinetic energy. since I had mass on both sides I canceled out the mass. I was then left with gh + (.5*26^2) = (.5*24^2).
 
  • #6
lauriecherie said:
I added the Kinetic energy plus the gravitational potential energy initial. I then set that equal to total mechanical energy final which only included kinetic energy. since I had mass on both sides I canceled out the mass. I was then left with gh + (.5*26^2) = (.5*24^2).

Ahhh. That explains it then.

You can't cancel out the mass.

You haven't accounted for the unknown work due to air resistance in your equation. You can't divide the mass out of that.
 

1. How does the Conservation of Energy apply to a ski-jump ramp?

The Conservation of Energy principle states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In the case of a ski-jump ramp, potential energy from the skier's initial position is transformed into kinetic energy as they slide down the ramp, and then into potential energy again as they reach the peak of their jump.

2. What factors affect the Conservation of Energy on a ski-jump ramp?

The main factors that affect the Conservation of Energy on a ski-jump ramp are the height of the ramp, the angle of the ramp, and the initial speed of the skier. These factors determine the amount of potential and kinetic energy present at different points on the ramp.

3. How does friction play a role in the Conservation of Energy on a ski-jump ramp?

Friction is a force that opposes motion and can cause energy to be lost. On a ski-jump ramp, friction between the skier's skis and the surface of the ramp can cause some energy to be lost as heat. This means that the skier may not reach the same height on their jump as predicted by the Conservation of Energy principle.

4. Are there any other forms of energy involved in a ski-jump ramp besides potential and kinetic energy?

Yes, there are other forms of energy involved in a ski-jump ramp, such as thermal energy from friction, and sound energy from the skier's movements and the noise they create. However, these forms of energy are relatively small compared to the potential and kinetic energy involved in the jump.

5. How does the Conservation of Energy impact the design of ski-jump ramps?

The Conservation of Energy principle is a key factor in designing ski-jump ramps. Engineers must consider the height, angle, and other factors to ensure that the ramp allows for the transformation of potential energy to kinetic energy, while minimizing energy loss due to friction. This results in ramps that are optimized for safety and performance.

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