After falling from rest from a height of 34 m, a 0.47 kg ball rebounds upward, reaching a height of 24 m. If the contact between ball and ground lasted 1.8 ms, what average force was exerted on the ball?
To find the average force exerted on the ball, we can use the principle of conservation of energy.
1. Find the gravitational potential energy before the fall:
The gravitational potential energy (PE) before the fall can be calculated using the equation PE = m * g * h, where m is the mass of the ball, g is the acceleration due to gravity, and h is the initial height.
Substituting the given values, we have PE_before = 0.47 kg * 9.8 m/s^2 * 34 m.
2. Find the gravitational potential energy after the rebound:
The gravitational potential energy after the rebound can be calculated using the same equation as above, but with the final height of the ball. In this case, h = 24 m.
So, PE_after = 0.47 kg * 9.8 m/s^2 * 24 m.
3. Find the change in gravitational potential energy:
The change in gravitational potential energy is simply the difference between the initial and final potential energies, given by ΔPE = PE_after - PE_before.
4. Find the work done on the ball during the contact with the ground:
The work done on the ball can be calculated using the equation W = F * d, where W is the work done, F is the average force exerted, and d is the displacement of the ball during the contact with the ground. In this case, d is the height from which the ball fell, i.e., 34 m.
So, W = F * 34 m.
5. Apply the principle of conservation of energy:
According to the principle of conservation of energy, the work done on the ball should be equal to the change in gravitational potential energy. Therefore, we have W = ΔPE.
6. Solve for the average force (F):
Equating the two equations from steps 4 and 5, we can find the average force:
F * 34 m = ΔPE.
Substituting the values, we have F * 34 m = (0.47 kg * 9.8 m/s^2 * 24 m) - (0.47 kg * 9.8 m/s^2 * 34 m).
Solving this equation for F will give us the average force exerted on the ball.
By following these steps, you can calculate the average force exerted on the ball.