# Efficiency of a hill

1. Jun 6, 2014

### Ltpenguin

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Efficency = (Power out) over (Power in)

3. The attempt at a solution

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

Thank you for your help :)

2. Jun 6, 2014

### dauto

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. Jun 6, 2014

### Ltpenguin

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. Jun 6, 2014

### CWatters

Consider how much energy the rider would have at the bottom if the ramp was 100% efficient.

5. Jun 6, 2014

### mafagafo

Also note that 400/980 = 0.41 (considering 2 sf)

6. Jun 6, 2014

### dauto

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.

7. Jun 6, 2014

### Ltpenguin

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. Jun 6, 2014

Yes indeed