A barefoot field-goal kicker imparts a speed
of 33 m/s to a football initially at rest.
If the football has a mass of 0.75 kg and the
time of contact with the ball is 0.015 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 the force exerted on an object is equal to the rate of change of its momentum.
Momentum (p) is defined as the product of mass (m) and velocity (v). In this case, the momentum of the football before it was kicked is zero because it was initially at rest.
Given:
Initial velocity of the football (u) = 0 m/s
Final velocity of the football (v) = 33 m/s
Mass of the football (m) = 0.75 kg
Time of contact with the ball (t) = 0.015 s
First, let's calculate the change in velocity (Δv):
Δv = v - u
Δv = 33 m/s - 0 m/s
Δv = 33 m/s
Next, we can use the formula for force (F) in terms of momentum:
F = Δp / t
The change in momentum (Δp) is equal to the product of mass and change in velocity:
Δp = m * Δv
Δp = 0.75 kg * 33 m/s
Δp = 24.75 kg m/s
Now we can calculate the force:
F = Δp / t
F = 24.75 kg m/s / 0.015 s
F ≈ 1650 N
Therefore, the force exerted by the ball on the kicker's foot is approximately 1650 Newtons.
To find the force exerted by the ball on the kicker's foot, you can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (p) with respect to time (t):
F = Δp / Δt
In this case, the momentum of the football is given by:
p = m * v
where m is the mass of the football and v is the velocity of the football after the kick.
Given:
- Mass of the football (m) = 0.75 kg
- Velocity of the football (v) = 33 m/s
- Time of contact (Δt) = 0.015 s
First, calculate the final momentum of the football:
p_final = m * v
p_final = 0.75 kg * 33 m/s
p_final ≈ 24.75 kg·m/s
Then, calculate the initial momentum of the football (since it was initially at rest, the initial momentum is zero):
p_initial = 0 kg·m/s
Now, calculate the change in momentum:
Δp = p_final - p_initial
Δp = 24.75 kg·m/s - 0 kg·m/s
Δp ≈ 24.75 kg·m/s
Finally, calculate the force exerted by the ball on the kicker's foot:
F = Δp / Δt
F = 24.75 kg·m/s / 0.015 s
F ≈ 1,650 N
Therefore, the force exerted by the ball on the kicker's foot is approximately 1,650 Newtons.