A football punter accelerates a football from rest to a speed of 9 m/s during the time in which his toe is in contact with the ball (about 0.22 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
To find the average force exerted on the ball by the punter, we can use Newton's second law of motion. According to the law, force is equal to the rate of change of momentum.
First, we need to calculate the initial momentum of the ball. Since the ball is at rest initially, its initial momentum is zero (p = mv, where p is momentum, m is mass, and v is velocity).
Next, we can calculate the final momentum of the ball using the equation p = mv. Given that the final velocity of the ball is 9 m/s and the mass is 0.50 kg, we can substitute these values to find the final momentum.
Final momentum (p) = 0.50 kg × 9 m/s = 4.5 kg·m/s
Now, we can calculate the change in momentum by subtracting the initial momentum (0) from the final momentum (4.5 kg·m/s).
Change in momentum = Final momentum - Initial momentum
= 4.5 kg·m/s - 0 kg·m/s
= 4.5 kg·m/s
To find the average force exerted on the ball, we divide the change in momentum by the time taken.
Average force (F) = Change in momentum / Time
= 4.5 kg·m/s / 0.22 s
≈ 20.45 N (rounded to two decimal places)
Therefore, the punter exerts an average force of approximately 20.45 N on the ball.