Impluse from spinning a wheel while standing on a skateboard

[robhlee]

Hello,
Say you have a frictionless setting. In this setting are two skateboards. One has a waterwheel (or any wheel with fins) propped up on beams so that it is on the skateboard and can freely turn. On the other skateboard is a person standing on it. If the skateboards are one behind the other (like train carts) and the person punches the wheel on a fin so that the wheel spins, the wheel will spin but neither skateboard will move.

What if you change the impulse of the punch from infinitesimal amount of time to say a few seconds?

 

[Doc Al]

If the skateboards are one behind the other (like train carts) and the person punches the wheel on a fin so that the wheel spins, the wheel will spin but neither skateboard will move.

Why do you keep saying this? Did the person exert a (horizontal) force on the wheel/skateboard: Yes! So you can deduce, from Newton's laws, that:
(1) The wheel/skateboard exerted an equal and opposite force on the person/skateboard. (Newton's 3rd law)
(2) Since this is the only force exerted (no friction to stop the skateboards from rolling) on each skateboard system, each system has a net force acting on it and it will accelerate. (Newton's 2nd law)

And why did you start a new thread on the same topic?

 

[robhlee]

well, its not exactly the same...I just had a question on the effect of impulse in this situation.

 

[Xezlec]

Yes but you're still making the mistake of stating that neither skateboard will move. They will both move.

This is more obvious if you draw a free-body diagram of the system and make sure you always draw paired forces because of Newton's 3rd Law.

In answer to your question about impulse, I think if the system is truly frictionless, time should make no difference. The reason this clashes with your intuition is that neither you nor I has ever seen anything remotely close to a frictionless system. In a system with friction, time could make a huge difference.

Also note that, even if pushing with the same force, you would have to exert more energy to push a skateboard by just pushing on the water wheel, compared with pushing directly on the skateboard. Why? Because work is force times distance, and since the wheel is moving as well as the skateboard, you have to push the fin a farther distance than the skateboard moves. The extra energy you expended then goes into the rotation of the water wheel.