Question

Suppose you toss a tennis ball upward.a) Does the kinetic energy of the ball increase or decrease as it moves higher?b) What happens to the potential energy of the ball as it moves higher?c) If the same amount of energy were imparted to a ball the same size as a tennis ball but of twicethe mass, how high would it go in comparison to the tennis ball?

Answer 1

Answer:

a) No. The kinetic energy of the ball decreases.

b) The potential energy of the ball increases.

c) The ball would go half of the original distance.

Explanation:

a) The kinetic energy would be converted to potential energy as the ball goes higher. Since the total mechanical energy is conserved, the kinetic energy would decrease.

b) The potential energy of the ball would increase. Since the total mechanical energy of the ball is conserved, the ball would lose speed, and therefore kinetic energy. In order to compensate the loss of kinetic energy, the ball would gain potential energy as it goes higher.

c) The relation of the energy and mass is as follows:

$K = \frac{1}{2}mv^2\\U = mgh$

According to the energy conservation

$K_1 + U_1 = K_2 + U_2\\\frac{1}{2}mv^2 + 0 = 0 + mgh\\\frac{1}{2}v^2 = gh$

The maximum height that the ball reaches is proportional to the initial velocity. If the ball would be imparted with the same amount of energy, its final potential energy would be the same. However, in order to have the same potential energy (mgh), its height would be half of the original case.

$mgh = (2m)g(\frac{h}{2})$