# Bicycle work question

1. Sep 7, 2008

### 40nni

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

If 2 bicyclists are cycling to the top of the same hill, and one bicyclist is using a gear that is twice as difficult as the other, is there a difference in work and power output between the 2 cyclists?

2. Sep 7, 2008

### LowlyPion

Welcome to PF.

What are your thoughts? Which of bicyclists would you bet on?

3. Sep 7, 2008

### 40nni

The fitter cyclist, every time!

I forgot an important constraint to my question - that both cyclists reach the top simultaneously.

Given that constraint, I'd guess both exert the same power (both output the same work over the same time).

Where I get hung up though, is that the cyclist who is mashing the pedals would be exerting more force over the same distance compared to the cyclist who is spinning faster. I suppose the force by the spinner is greater than I perceive given the greater number of repetitions.

Anecdotally, mashing on a high geared singlespeed is tougher, but I suppose it's all how you train you legs.

4. Sep 7, 2008

### LowlyPion

You've answered your own question then, at least as far as your constraint. If everything else is equal, like their weight, the net work they both must do is given by m*g*h. If you constrain them to arrive at the same time, then you have constrained them to go at the same speed. The wheels of each must revolve at the same speed with your constraint.

The lower gear will make fewer revolutions of the pedal, but the cyclist must push more forcefully, then to achieve the same progress on the road.

If there is a difference then maybe it's in the bio-physics of the cyclists themselves? One cyclist will have twice the repetitions with his legs to go the same distance over and above the power he delivers to the bike moving forward.