# Conservation of mechanical energy: Cyclist up a hill

1. Oct 21, 2008

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

A cyclist intends to cycle up a 8.00 hill whose vertical height is 115 . The pedals turn in a circle of diameter 36.0 .

1:Assuming the mass of bicycle plus person is 80.0 , calculate how much work must be done against gravity.

2: If each complete revolution of the pedals moves the bike 5.90 along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.

2. Relevant equations
1: W = F*d

2: I dont know. Somehow I am sure it involves 1/2mv^2 + mgy

3. The attempt at a solution

1: W= (80kg*9.8m/s)*115m = 90160 N*m = 9.02*10^4 J (this one I solved)

2: shrug

2. Oct 21, 2008

### LowlyPion

Welcome to PF.

You can't get the right answer without the right units.

3. Oct 21, 2008

Ack!!. The first attempt to post I had all the units. I hurridly relaid it out.

8.00 Degrees
115m
36.0 cm Breaks down into .36 m with a radii of .16 m
80.0 kg
5.90 m

and the onyl equation I can assume for 2 is 1/2 mv^2+mgy

4. Oct 21, 2008

### LowlyPion

Perhaps you can approach 2) by identifying how much increase in Potential Energy for each revolution. Then knowing that amount of work to do that and the distance over which you had to do it ...

5. Oct 21, 2008

W = (80kg*9.8m/s)*(5.90m/2pi.16) = 1160 J ??

I am not understanding at all. I can believe I am being stumped by this when I could get the complete total for #1

6. Oct 21, 2008

### LowlyPion

Well what's a joule? A N-m

And the increase in Y is what determines your increase in PE.

So doesn't that mean that your increase in PE/5.9 = Favg ?