A 220-g ball strikes a wall with a speed of 7.0 m/s and rebounds with only 37% of its kinetic energy. What is the speed of the ball immediately after rebounding?
What is the magnitude of the impulse of the ball on the wall?
If the ball was in contact with the wall for 9.9 ms, what is the magnitude of the average force exerted by the wall on the ball during this time interval?
KE2=0.37KE1
(m(v2)^2)/2=0.37(m(v1)^2)/2.
The speed of the ball immediately after rebounding is
v2=v1(sqroot(0.37)) =0.6•7=4.2 m/s.
The magnitude of the impulse of the ball on the wall:
delta(p) = p2 - p1= mv2 - (- mv1) = mv2 + mv1=
m(v2+ v1) = 0.22•(4.2 + 7) = 2.464 kg•m/s.
The magnitude of the average force
exerted by the wall on the ball during this time interval:
F•delta(t) = delta(p),
F= delta(p)/ delta(t) = 2.464/9.9=0.249 N.
Thanks. the impulse is correct but the magnitude of the average force is not.
To calculate the speed of the ball immediately after rebounding, we need to use the principle of conservation of kinetic energy.
1. First, let's calculate the initial kinetic energy (KE_initial) of the ball. We know that the mass (m) of the ball is 220 grams, which is 0.22 kg, and the initial speed (v_initial) is 7.0 m/s. The formula for kinetic energy is KE = 1/2 * m * v^2.
KE_initial = 1/2 * 0.22 kg * (7.0 m/s)^2
2. Next, let's calculate the final kinetic energy (KE_final) of the ball after rebounding. We know that the final kinetic energy is only 37% of the initial kinetic energy.
KE_final = 37% * KE_initial
3. Now, let's calculate the speed (v_final) of the ball after rebounding using the final kinetic energy. Rearranging the kinetic energy formula, we get v = √(2 * KE / m).
v_final = √(2 * KE_final / m)
4. Calculate the final speed of the ball using the calculated values.
v_final = √(2 * KE_final / m)
To find the magnitude of the impulse of the ball on the wall, we can use the impulse-momentum theorem, which states that the impulse is equal to the change in momentum. Impulse (J) is given by the equation J = m * Δv, where Δv is the change in velocity.
1. The change in velocity (Δv) is equal to the final velocity minus the initial velocity. We can use the speed to calculate the magnitude of the velocity.
Δv = v_final - v_initial
2. Calculate the magnitude of the impulse using the formula J = m * Δv.
J = m * Δv
To find the magnitude of the average force exerted by the wall on the ball during the contact time, we can use the equation F = J / Δt, where Δt is the contact time.
1. Use the calculated value of the impulse (J) and the contact time (Δt) to calculate the magnitude of the average force (F).
F = J / Δt