A barefoot field-goal kicker imparts a speed of 47 m/s to a football initially at rest.
If the football has a mass of 0.6 kg and the time of contact with the ball is 0.024 s, what is the magnitude of the force exerted by the ball on the kicker’s foot?
300N
To find the magnitude of the force exerted by the ball on the kicker's foot, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the acceleration is the change in velocity of the football.
First, calculate the change in velocity:
Δv = final velocity - initial velocity
Δv = 47 m/s - 0 m/s
Δv = 47 m/s
Next, calculate the acceleration:
acceleration = Δv / time
acceleration = 47 m/s / 0.024 s
acceleration ≈ 1958.33 m/s²
Now, we can use Newton's second law to find the force:
force = mass × acceleration
force = 0.6 kg × 1958.33 m/s²
force ≈ 1175 N
Therefore, the magnitude of the force exerted by the ball on the kicker's foot is approximately 1175 Newtons.