Calculate Efficiency of Hill for Snowboarder

In summary, the snowboarder's efficiency going down the ramp is 41%, calculated by dividing the useful energy output (580J) by the total mechanical energy at the top of the hill (980J). This means that 59% of the energy was lost during the descent. The energy at the bottom of the hill (400J) is not waste, but rather the reason the snowboarder was able to go down the hill in the first place. Similarly, in the example of a 1000w light bulb with 750w wasted energy, the efficiency would be 25%.
  • #1
Ltpenguin
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Homework Statement



A snowboarder goes down a ramp when initially at rest. The Total mechanical energy on top of the hill is 980 J and 400J at the bottom of the hill. Calculate efficiency of the ramp.

Homework Equations



Efficency = (Power out) over (Power in)

The Attempt at a Solution


Tw7Baph.png


I believe the %59 is correct because at the bottom of the hill the snowboarder had 400 J of energy left ( waste energy) so that is not calculated in efficiency you use 980-400 = 580J is the useful energy out. is this correct?

or is it this
QfPboFE.png

Thank you for your help :)
 
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  • #2
The second solution makes more sense to me. By the way, the correct form is Eff. = 41%, not %Eff. = 41 which makes no sense.
 
  • #3
dauto said:
The second solution makes more sense to me. By the way, the correct form is Eff. = 41%, not %Eff. = 41 which makes no sense.

Well % efficiency = 41 % yes. Although i still think since you calculate the efficiency of the hill any left over energy (400J)at the bottom of the hill is considered waste. Since you only calculate useful power output in efficiency you shouldn't use the remaining energy for your equation but the difference i.e. 580J was used to go down the hill. Hope i am explaining it correctly.
 
  • #4
To help you decide which calculation is correct...

Consider how much energy the rider would have at the bottom if the ramp was 100% efficient.
 
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  • #5
Also note that 400/980 = 0.41 (considering 2 sf)
 
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  • #6
Ltpenguin said:
Well % efficiency = 41 % yes. Although i still think since you calculate the efficiency of the hill any left over energy (400J)at the bottom of the hill is considered waste. Since you only calculate useful power output in efficiency you shouldn't use the remaining energy for your equation but the difference i.e. 580J was used to go down the hill. Hope i am explaining it correctly.

No, not % efficiency = 41 %. As I said that is not correct. The correct way is efficiency = 41%. Keep in mind that % is just a shorthand for (1/100). Than if efficiency = 0.41 we have

Efficiency = 0.41 = 41/100 = 41*(1/100) = 41%.

There is no % sign before the word efficiency. That's just wrong.

Also, the Mechanical energy at the bottom of the hill is the reason snowboarders like going down a hill. It makes no sense to call it waste since that energy was the motivation to go uphill to begin with. that 41% is the useful energy. The waste is the 59% that was lost along the way down the hill.
 
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  • #7
First thank you all for the help :) i was wondering if a 1000w light bulb had 750w wasted energy then i would calculate the light bulb as having only 250w of useful energy so 250w over 1000w? 25 % efficiency?
 
  • #8
Ltpenguin said:
First thank you all for the help :) i was wondering if a 1000w light bulb had 750w wasted energy then i would calculate the light bulb as having only 250w of useful energy so 250w over 1000w? 25 % efficiency?

Yes indeed
 
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1. How is efficiency of hill calculated for a snowboarder?

The efficiency of hill for a snowboarder is calculated by dividing the distance traveled by the snowboarder by the elevation change of the hill. This ratio is then multiplied by 100 to get a percentage value.

2. Why is it important to calculate the efficiency of hill for a snowboarder?

Calculating the efficiency of hill for a snowboarder can help them determine which hills are best suited for their skill level and physical abilities. It can also help them track their progress and identify areas for improvement.

3. What factors can affect the efficiency of hill for a snowboarder?

The efficiency of hill for a snowboarder can be affected by factors such as the snow conditions, the steepness and length of the hill, the shape and size of the snowboard, and the skill level and technique of the snowboarder.

4. Is it possible to improve the efficiency of hill for a snowboarder?

Yes, the efficiency of hill for a snowboarder can be improved through practice, proper technique, and using equipment that is suitable for the snow and terrain conditions. Strengthening the muscles used in snowboarding can also improve efficiency.

5. How can knowing the efficiency of hill benefit a snowboarder?

Knowing the efficiency of hill can benefit a snowboarder by helping them plan their rides and choose the best routes for their skill level. It can also help them conserve energy and reduce the risk of injury by avoiding hills that are too challenging for them.

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