[Physics] Why does a Ball bounce back if Forces are Equal and Opposite

collisionconservation-lawsforcesmomentumnewtonian-mechanics

When a ball is thrown onto a wall, the ball exerts a force onto the wall. According to Newton's Third Law, the wall will exert an equal and opposite force to the ball. Thus, how would the ball be able to bounce back? Shouldn't it just slide down the wall?

Best Answer

You have to consider this as a dynamic process. To make sense of it you also have to think of the ball as NOT a point particle, so it has a centre of gravity, probably in its actual centre. As the surface of the ball impacts the wall the centre of gravity slows down, which means its momentum drops. (It also means that the wall or the ball or both must deform during the impact) Newton's second law requires that momentum can only change if there is an external force applied and this comes from the wall. This force increases from zero as the impact proceeds, it is exerted in the opposite direction of the balls motion. At some point the momentum will reach zero, but the force is still there and still directed outwards so now it begins to accelerate the ball's centre of gravity back in the opposite direction. As it moves out the balls momentum increases and the force drops but still points in the same direction. So the ball accelerates until the surfaces separate at which point the force is back to zero.

Now it is true that Newton3 requires that throughout this process the ball is exerting an equal and opposite force on the wall but the point here is that these two forces are exerted on DIFFERENT objects. So the force of the ball on the wall acts to try and increase the momentum of the wall (if it was somehow moveable it would accelerate away from the impact). For a fixed wall the force goes to make some deformation of the wall (bending it / making a dent in it etc.)

If both objects are perfectly elastic, meaning they return to their original shape once forces are removed, then the ball will rebound with exactly the same but opposite momentum it had before the impact. If either object is permanently deformed in the impact, the ball will rebound with less momentum.

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