A barefoot field-goal kicker imparts a speed
of 39 m
/
s to a football initially at rest.
If the football has a mass of 0
.
26 kg and the
time of contact with the ball is 0
.
01 s, what
is the force exerted by the ball on the kicker’s
foot?
To find 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 the rate of change of momentum.
The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the football is 0.26 kg and the velocity it acquires from the kicker is 39 m/s.
First, calculate the momentum of the football:
Momentum = Mass × Velocity
Momentum = 0.26 kg × 39 m/s
Momentum = 10.14 kg·m/s
Now, we can use the concept of impulse, which is the change in momentum, to find the force exerted by the ball on the kicker's foot. Impulse is equal to the force applied multiplied by the time of contact.
Impulse = Force × Time
Solving for force, we have:
Force = Impulse / Time
Since we have the momentum, we can calculate the impulse using the change in momentum:
Impulse = Final momentum - Initial momentum
Impulse = Momentum - 0 (since the ball is initially at rest)
Impulse = 10.14 kg·m/s
Finally, we can calculate the force:
Force = Impulse / Time
Force = 10.14 kg·m/s / 0.01 s
Force = 1014 N
Therefore, the force exerted by the ball on the kicker's foot is 1014 Newtons.