Torque vs force

1. Dec 18, 2004

ponjavic

Ok I have built this car for a school project that is supposed to go against the wind. As there is a wind it should be able to drive into it (powered by the wind).

Now the car is built and it is working. I have mounted a horizontal windmill that through gearing powers the back wheels.

What I wonder is, why is the the torque, or for constant velocity the angular momentum, greater than the drag on the car?

2. Dec 18, 2004

Andrew Mason

Interesting question. In fact, it is a great question.

Since forces act in equal and opposite pairs, one might think that the force of the wind against the car could not be less than the force of the car against the wind. One can think of an analogy of someone firing cannonballs at the car and the car capturing those canonballs to move toward the cannonballs. It seems to defy conservation of momentum.

The answer has to do with the difference between energy and momentum. The car is driven by wind energy, not its momentum.

Let's look at my example of the cannonballs. Imagine that the car captures the cannonball with a pocket mounted at the end of a horizontal arm. This causes the arm to spin around (like your windmill) converting the cannonball's kinetic energy into rotational kinetic energy. Linear momentum of the cannonball is transferred to the car and the car experiences an impulse to the rear (ie. in the direction of the original cannonball). This can never be avoided. But if the cannonball has a mass that is 1/100th of the mass of the car, the rearward speed of the car due to the cannonball impulse is 1/100th of the speed of the cannonball. So, and this is the critical issue: the car's rearward kinetic energy due to its capture of the canonball is $1/2mv^2$ so it is 100 x 1/10,000th or 1/100th of the energy of the cannonball. Since the rest of the cannonball energy has been stored in the rotating arm, the car can use this energy to move forward. And it does.

Think of the wind as continuous cannonballs. There are other factors, of course, such as wind resistance. But these depend on the design of the car and can be managed.

AM

3. Dec 19, 2004

ponjavic

Sweet comparison, yeah a constant flow of cannonballs would also hit the car itself but off course the pockets were the main issue.
thank you very much!