A 564 g ball strikes a wall at 12.8 m/s and rebounds at 10.4 m/s. The ball is in contact with the wall for 0.038 s.
What is the magnitude of the average force acting on the ball during the collision?
Answer in units of N.
To find the magnitude of the average force acting on the ball during the collision, we can use the formula for average force:
Average Force = Change in Momentum / Time
First, let's calculate the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum
The final momentum can be calculated by multiplying the mass of the ball (m) with the velocity after the rebound (vf):
Final Momentum = m * vf
Similarly, the initial momentum can be calculated by multiplying the mass of the ball (m) with the initial velocity (vi):
Initial Momentum = m * vi
Now, let's substitute the given values into the formulas:
m = 564 g = 0.564 kg (converting to kilograms)
vi = 12.8 m/s
vf = -10.4 m/s (negative sign due to rebound)
Now we can calculate the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum
= m * vf - m * vi
= m * (vf - vi)
Substituting the values:
Change in Momentum = 0.564 kg * (-10.4 m/s - 12.8 m/s)
= 0.564 kg * (-23.2 m/s)
= -12.7488 kg*m/s
Next, we need to calculate the average force by dividing the change in momentum by the time of contact:
Average Force = Change in Momentum / Time
Given: Time = 0.038 s
Average Force = -12.7488 kg*m/s / 0.038 s
= -335.5 N (rounded to the nearest whole number)
Therefore, the magnitude of the average force acting on the ball during the collision is approximately 336 N.