Does Turning Off the Lamp on a Push Bike Increase Coasting Distance?

[pivoxa15]

Homework Statement

The dynamo (generator) of a push bike is made to turn when the bicycle wheel turns. The generator provides energy to light the bicycle’s lamp. Would a cyclist coast further if the lamp connected to the generator were turned on or off? Why?

Homework Equations

The Attempt at a Solution

If on then power is dissipated via P=I^2R so some energy from the peddler is given to powering the light.

If off then no power is lost and the generator will turn by itself (although some energy is lost to friction which must come from the peddler) after it has turned a cycle. This is because potentials get accumulated on the ends of the disconnected ciruit and can be reversed to allow for the induced emf in direction and magnitude. Hence if the peddler supplies the same amount of energy as the first case of lamp turned on then a lot more percentage of energy is turned into motion of the bike. So coast further with lamp turned off.

 

[Kurdt]

You are right but I'm not sure of your explanation. Basically with the generator on it is obviously removing energy from the motion of the bike (that is why the light is on) whereas with the generator off the bike only loses energy to friction and thus will coast further.

 

[pivoxa15]

Why is the generator off? When the switch is off, it dosen't mean the generator is off or does it? Or you mean when the generator doesn't carry current to a load, it is considered off. In the problem, the generator will always spin when the man is pedaling. The generator would still rotate but no significant power is dissipated. The current will flow in half a cycle in one direction and another direction in the other half cycle but with much less power dissipatted since the current doen't go to power any load. So the reason could be easier than what I stated in my OP.

 

[Kurdt]

I suppose it depends what kind of dynamo you use. All the ones I've seen when you want to turn them off you just move them awa from the wheel so they are no longer in contact. This happens for the obvious reason that the extra friction caused by it makes it more difficult to pedal.