Question #23d47
1 Answer
I rewrote your question significantly. I think it is clearer, but if this doesn't answer your question, please ask again.
The reason you can push the car and remain stationary, is that there is another force pushing on you. Your feet are in contact with the road and, if your shoes don't slip, a force equal to the force you exert on the car is being exerted on the road by your feet. It is in the opposite direction. The net force on you is zero and you do not move.
Now think about the situation where the road is very icy. If the car is moving and tries to stop, it will just keep moving. If the car is stopped, it requires very little force to get it moving. However, without traction on the road, your attempts to push it by hand will just result in you being pushed away from the car. If there is really no friction, the car will move and you will move. In this case you will move a lot faster than the car. The velocity of both you and the car can be calculated from simple conservation of momentum.
In the case where you are pushing on the ground, you could calculate the change in momentum of the entire earth. For any measurement you would try to make, this can be considered to be an infinite mass compared to the car. Theoretically, the earth moves in reaction to the acceleration of the car. Experimentally, you'd have a tough time proving that.
