A tennis ball of 60g is dropped from a height of 2.0m,It rebounds but loses 25% of its kintic energy as thermal energy.Ignoring air resistance,calculate
(1)the kinetic energy of the tennis ball when hits the ground.
(2)the height reached on the ground
(1) Before or after bouncing?
(2) How can the ball reach a height while on the ground?
The ball has a kinetic energy equal to M*g*H just before bouncing
To answer these questions, we need to understand the principle of conservation of energy. The total mechanical energy of an object remains constant if there is no external force working on it.
Let's break down the problem step by step.
First, we need to find the initial potential energy of the tennis ball when it is dropped from a height of 2.0m. The potential energy (PE) is given by the formula:
PE = mgh
Where:
m = mass of the ball (60g = 0.06kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height (2.0m)
So, the initial potential energy (PEi) is:
PEi = 0.06kg * 9.8 m/s^2 * 2.0m
Next, we need to find the initial kinetic energy of the tennis ball when it hits the ground. Since the ball is dropped, it has no initial kinetic energy, so KEi = 0.
Upon hitting the ground, the tennis ball rebounds. However, it loses 25% of its kinetic energy as thermal energy. The remaining kinetic energy (KEr) is therefore 75% of the initial kinetic energy.
Now, we can calculate the remaining kinetic energy (KEr) using the formula:
KEr = 0.75 * KEi
Since KEi is 0, KEr is also 0.
Finally, we can find the height (h') reached by the ball after rebounding.
Applying the principle of conservation of mechanical energy, the sum of the potential energy and kinetic energy after rebounding (PE' + KEr) is equal to the initial potential energy (PEi):
PE' + KEr = PEi
Since KEr is 0, the equation becomes:
PE' = PEi
Using the formula for potential energy, we can solve for h':
h' = PEi / (m * g)
Substituting the known values:
h' = (0.06kg * 9.8 m/s^2 * 2.0m) / (0.06kg * 9.8 m/s^2)
Simplifying:
h' = 2.0m
Therefore, the height reached by the tennis ball after rebounding is also 2.0m.
Recapping the answers:
(1) The kinetic energy of the tennis ball when it hits the ground is 0 J.
(2) The height reached by the tennis ball on the ground is 2.0m.