# Momentum and impulse of a football

• ac7597
In summary, Joe Varsity exerts a maximum force of 6250N on a 0.9kg football over 5 milliseconds, giving it an impulse of 31.25 J. The ball's speed immediately after the kick is 11.57 m/s. To calculate the impulse, the force formula should be integrated over the time interval of 0.005 seconds and then use the momentum-impulse theorem to find the momentum and velocity of the ball. The correct unit for impulse is N*s.
ac7597
Homework Statement
Joe Varsity kicks a football of mass 0.9 kg. As his foot makes contact with the ball, it exerts a force which gradually increases to a maximum value over 5 milliseconds, then falls immediately to zero, as shown in the graph above. The force is given by the equation:
Force=(250 Newtons)∗(t/t0)^2
where t0 equals 1 millisecond.

What is the impulse given by Joe's foot to the ball? Don't forget the units

The ball was originally sitting on the tee, motionless. What is its speed immediately after Joe kicks it?
Relevant Equations
average force= impulse/(time)
Homework Statement: Joe Varsity kicks a football of mass 0.9 kg. As his foot makes contact with the ball, it exerts a force which gradually increases to a maximum value over 5 milliseconds, then falls immediately to zero, as shown in the graph above. The force is given by the equation:
Force=(250 Newtons)∗(t/t0)^2
where t0 equals 1 millisecond.

What is the impulse given by Joe's foot to the ball? Don't forget the units

The ball was originally sitting on the tee, motionless. What is its speed immediately after Joe kicks it?
Homework Equations: average force= impulse/(time)

Since impulse= (average force)*time
average force= (250 Newtons)∗(0.005s /1 milliseconds)^2= 6250N
impulse= (0.005 s)(6250N)= 31.25 J
Is J the right unit or is it N*s ?

momentum= (mass)(velocity)
momentum immediately after Joe kicks the ball= (250 Newtons)∗(0.001s /1 milliseconds)^2 * (0.001s) = 0.250N
0.250N = (0.9kg)(velocity)
velocity=0.278 m/s

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First what you calculate as average force, is NOT the average force at all, it is rather the maximum force which is the force at time t=0.005sec. Also I think that to find impulse you should integrate the force formula over the time interval of 0.005sec that is you should consider the integral $$\Omega=\int_0^{0.005}250\cdot (\frac{t}{t_0})^2dt$$
After you calculate that integral, use the momentum-impulse theorem that is
$$\Delta J=J_{after}-J_{before}=\Omega$$ and you should be able to calculate the momentum and the velocity of the ball after the kick.

Ω= 250N(1/0.001)^2 ∫(t^2) dt
Ω=(250*10^6) * (t^3)/3 with t=0.005 and t=0
Ω=10.417-0=10.417N*s

10.417N*s= (0.9kg)(velocity)
velocity=11.57m/s
Thanks!

## 1. What is momentum and impulse?

Momentum is the measure of an object's motion, determined by its mass and velocity. Impulse is the change in momentum that occurs when a force is applied to an object.

## 2. How is momentum and impulse related to a football?

In the context of a football, momentum and impulse refer to the force and movement of the ball during a game. When a player kicks or throws the ball, they are applying a force and causing a change in the ball's momentum.

## 3. Why is momentum important in football?

Momentum is important in football because it determines the speed and direction of the ball during a game. The more momentum the ball has, the harder it is for the opposing team to stop or change its trajectory.

## 4. How does the mass and velocity of a football affect its momentum?

The mass and velocity of a football directly affect its momentum. The greater the mass and velocity of the ball, the greater its momentum will be. This is why a heavier or faster-moving ball can be more challenging for players to stop or control.

## 5. How can momentum and impulse be used to improve a football player's performance?

Understanding momentum and impulse can help a football player improve their performance by allowing them to control the ball more effectively. By adjusting their kicking or throwing technique, a player can increase the ball's momentum and improve its speed and accuracy.

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