The Physics of Basketball

Draw the free body diagram for a jumping basketball player (a) just before leaves the ground and (b) while he is in the air. Indicate qualitatively the size of the forces involved.

a) While the basketballer is on the ground, he is subject to two forces, gravity, pushing him downwards, and the “normal” or “reaction” force of the ground upwards on his feet (He pushes down on the ground through his feet, and from Newton’s Third Law, we know that the ground pushes up on his feet with a force of the same magnitude).

As he is in the middle of leaping, his torso is already moving upwards with some velocity, and if he intends to leap to any reasonable height, this velocity will be increasing as he straightens his legs. Thus, the player’s center of mass is accelerating upwards, indicating that he is experiencing a net force upwards. Ie, the Normal force is greater than the gravitational force. (of mg, where m is the player’s mass)

You might worry that this violates Newton’s third law, but it is important to remember that the action-reaction pairs of Newton’s laws always act on different objects – the Normal and Gravity are not such a reaction pair. The reaction partner of the gravitational force in this case is a gravitational force of mg pulling the earth towards the basketballer, and a force equal to the normal force, but downwards, due to the basketballer pushing the earth away.

The free body diagram of the jumping basketball player is figure 1, left.



 

b) The instant the basketballer looses contact with the ground the normal force vanishes – without the contact there is no way for the earth to directly push on the player. Gravity, however, acts through the gravitational field and can affect objects that are separated from the earth – which is fortunate, or else no object that left the ground would ever come back down, and our atmosphere would have floated away long before we evolved (in fact, without gravity, neither the earth nor any of the heavenly bodies would have ever formed in the first place).