A football punter accelerates a football from rest to a speed of 9.1 m/s
during the time in which his toe is in contact with the ball (about 0.247 s). If the football
has a mass of 484 g, what average force does the punter exert on the ball?
Impulse momentum equation. From Newtons second law, F=MA. Since acceleration (A) is Change in velocity/time, the equation turns into F=M[(Vf-Vi)]/t. Multiplying both sides of the equation by t gives you Ft=M(Vf-Vi). Since initial velocity is 0, the equation turns into Ft=MVf. Rearranging the equation, to solve for F turns the equation into F=MVf/t, plug in your values for t, Vf, and M, resulting in a rearranged formula looking like F= [(0.484Kg)(9.1m/s)]/(0.247s). Solve for F. Note that I converted g to Kg first before solving.
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 is equal to the mass of the object multiplied by its acceleration.
First, we need to calculate the acceleration of the football. The initial velocity is zero since the football starts from rest, and the final velocity is 9.1 m/s.
Using the formula:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange the formula to solve for the acceleration, a:
a = (v - u) / t
Substituting the given values:
a = (9.1 m/s - 0 m/s) / 0.247 s
a = 9.1 m/s / 0.247 s
a ≈ 36.86 m/s²
Next, we can calculate the force using Newton's second law:
F = m * a
where F is the force, m is the mass of the football, and a is the acceleration we just calculated.
Given that the mass of the football is 484 g, which is equal to 0.484 kg:
F = 0.484 kg * 36.86 m/s²
F ≈ 17.88 N
Therefore, the average force exerted by the punter on the ball is approximately 17.88 Newtons.