a football punter accelerates from rest to a speed of 8 m/s during the time in which his toe is in contact with the ball (about 0.21 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
The punter himself does not accelerate. The football does. So does his foot, but not as much as the ball does. If his own center of mass accelerated to 8 m/s in 0.21 seconds, we would be a world class sprinter.
The momentum change of the football,
8 m/s * 0.50 kg = 4.0 kg m/s
is equal to the impulse, F*0.21 s.
Solve for F.
To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force exerted on the ball by the punter's foot is what accelerates the ball.
First, we need to find the acceleration of the ball. Since the punter starts from rest and reaches a final speed of 8 m/s in 0.21 seconds, we can use the equation for average acceleration:
acceleration (a) = (change in velocity)/(time)
The change in velocity is 8 m/s - 0 m/s = 8 m/s, and the time is 0.21 s. Substituting these values into the equation:
a = 8 m/s / 0.21 s = 38.1 m/s²
Now we can find the force exerted by the punter on the ball using Newton's second law:
force (F) = mass (m) * acceleration (a)
Given that the mass of the ball is 0.50 kg and the acceleration is 38.1 m/s²:
F = 0.50 kg * 38.1 m/s² = 19.05 N
Therefore, the average force exerted by the punter on the ball is 19.05 Newtons.