A tennis ball is hit into the wall with a speed of 26 m/s.
If it rebounds with a speed of 24 m/s, how much energy was lost in the collision?
mass of tennis ball = 0.059 kg
A) 6 joules
B) 1 joule
C) 3.0 joules
whoops
add 26 + 24 correctly when doing (a^2-b^2) =(a-b)(a+b)
=.0295 (2)(50)
around 2.95 Joules
(1/2)(.059) (26^2-24^2)
=.0295 (2)(48)
around 2.9 Joules
To determine how much energy was lost in the collision, we can use the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant if no external forces are acting on it.
In this case, the mechanical energy of the tennis ball before the collision (when it was initially hit) can be calculated using the formula:
E_initial = 0.5 * mass * velocity_initial^2
where:
- E_initial is the initial mechanical energy (before the collision).
- mass is the mass of the tennis ball.
- velocity_initial is the initial velocity of the tennis ball before the collision.
Similarly, the mechanical energy of the tennis ball after the collision (when it rebounds) can be calculated using the formula:
E_final = 0.5 * mass * velocity_final^2
where:
- E_final is the final mechanical energy (after the collision).
- velocity_final is the velocity of the tennis ball after the collision.
To determine the amount of energy lost in the collision, we can subtract the final energy from the initial energy:
Energy_lost = E_initial - E_final
Now let's calculate the values:
mass = 0.059 kg
velocity_initial = 26 m/s
velocity_final = 24 m/s
E_initial = 0.5 * 0.059 kg * (26 m/s)^2
E_final = 0.5 * 0.059 kg * (24 m/s)^2
Energy_lost = E_initial - E_final
Calculating these values, we find:
E_initial ≈ 22.588 J
E_final ≈ 16.96 J
Energy_lost ≈ 22.588 J - 16.96 J ≈ 5.628 J
Therefore, approximately 5.628 joules of energy was lost in the collision.
Since none of the multiple-choice options perfectly match the calculated value, we can round to the nearest whole number. Thus, the answer would be 6 joules (option A).