Wize University Physics Textbook (Master) > Momentum, Impulse and Collisions

Linear Momentum and Impulse

Linear Momentum and Impulse

Linear Momentum

Linear Momentum (or simply Momentum) is defined as the product of mass and velocity of an object.

Momentum is a vector and measured in kg . m/s.

\boxed{\vec{P}=m\vec{v}}

If a force is applied to an object, the Second law of Newton could be written in terms of change in momentum as follows:

\vec{F}=m\vec{a}\ \ \ \ \ \ \ \ \ \rightarrow\ \ \ \ \ \ \ \ \ \ \ \ \vec{F}=m\frac{\Delta v}{\Delta t}

Impulse

Impulse is defined as the change in the momentum of the object if a constant external force of F is applied to the object:

\boxed{\vec{J}\ =\Delta\vec{P}\ \ =\vec{F}\Delta t}

Linear Momentum and Impulse

Linear Momentum

Linear Momentum (or simply Momentum) is defined as the product of mass and velocity of an object.

Momentum is a vector and measured in kg . m/s.

\boxed{\vec{P}=m\vec{v}}

If a force is applied to an object, the Second law of Newton could be written in terms of change in momentum as follows:

\vec{F}=m\vec{a}\ \ \ \ \ \ \ \ \ \rightarrow\ \ \ \ \ \ \ \ \ \ \ \ \vec{F}=m\frac{\Delta v}{\Delta t}

\vec{F} = \frac{d\vec{p}}{dt}

Impulse

Impulse is defined as the change in the momentum of the object if a constant external force of F is applied to the object:

\boxed{\vec{J}\ =\Delta\vec{P}\ \ =\vec{F}\Delta t}

For a net external force which is changing in time, impulse is defined as below:

\boxed{\vec{J}=\Delta\vec{P}=\int_{t_i}^{t_f}\vec{F}\left(t\right)dt}

Example: Impulse to a Soccer Ball

A soccer player applies an average force of 180 N during a kick. The kick accelerates a 0.45 kg soccer ball from rest to a speed of 18 m/s. What is the impulse imparted to the ball? What is collision time?

Solution:

We know that impulse is defined as:

$J = \Delta p = p_f-p_i=F_{avg}\Delta t$

Since the ball is at rest before the kick, its initial momentum is zero.

$p_i =0$

So, we can easily calculate impulse as:

$J = p_f = mv_f$

$J = (0.45)(18) = 8.1\ kg .m/s$

Furthermore, we can find the time duration of the kick again by looking at the definition of impulse:

$J = F_{avg} \Delta t$

$\Delta t =\dfrac{J}{F_{avg}}$

$\Delta t = \dfrac{8.1}{180}= 0.045\ sec$

A 2.5 kg Dodge ball hits the back wall of a school gym at 15 m/s at an angle of 50º to the wall. The ball is in contact with the wall for 0.15s before bouncing back at 12 m/s at an angle of 60º to the wall. What average force was exerted by the ball on the wall?

Illustration for practice question: Impulse on a Dodge Ball

A) 370 N

B) 420 N

C) 468 N

D) 569 N

I don't know

A force $F=(2t^2-5) N$ is acting on a moving object with mass of 2kg in the direction of its motion for 5 seconds. If the initial speed of the particle is 5m/s.

a) What is the final momentum of the object? b) What is the impulse?

I don't know

Extra Practice

Particle m1 with mass of $4 \times 10^{-25}$ kg is travelling with a velocity of $5\frac{m}s\hat i$ , and collides with particle m2 with mass $6\times 10^{-25}~\rm kg$ which is initially at rest. After the interaction, m1 travels with speed of 5 m/s at an angle of 45 degrees with vector.

What is the total momentum of the system?
What is the vector velocity of m2?

impulse

A soccer player applies an average force of 180 N during a kick. The kick accelerates a .45 kg soccer ball from rest to a speed of 18 m/s. What is the impulse imparted to the ball? What is collision time?

momentum, impulse

A heavy truck has more momentum than a passenger car moving at the same speed because the truck

momentum impulse

A heavy object and a light object have the same momentum. Which has the greater speed?

momentum impulse

A boxer quickly learns to move his head backward when he sees he is going to receive a jab to the head. What does this head motion accomplish?

momentum

How can you increase the linear momentum of something?

Impulse and momentum

A 1.0 kg body, initially at rest, is acted on by the horizontal force shown in the graph. What is its speed in m/s when t=8 s? Illustration for practice question: Impulse and momentum

A bat strikes a 0.145-kg baseball. Just before impact is traveling horizontally to the right at 50 m/s ,and it leaves the bat traveling to the left at an angle of $30^{\circ}$ above horizontal with a speed of 65 m/s. If the ball and bat are in contact for 1.75 ms, find the horizontal and vertical components of the average force on the ball.

10-gram bullet is hitting a thick wood target with velocity 600 m/sec and penetrates through it. The diagram below shows the force applied to the bullet as function of time. What is the velocity of the bullet as it leaves the target from other side?

A 50-grams rubber ball is dropped from a height of 4 m. It hits the ground and bounces up, rising to height of 3.2 m. If the impact with ground only takes 0.05 second, what is the average force acting on the ball during the impact?

For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 miles/h). If the ball has a mass of 0.060 kg and is in contact with the racket for about 4 ms $(4\times 10^{-3}~\rm s)$ , estimate the average force on the ball.

Practice: Momentum (impulse) with calculus

A force $F=(2t^2-5) N$ is acting on a moving object with mass of 2kg in the direction of its motion for 5 seconds. If the initial speed of the particle is 5m/s.

Practice: Dodgeball impulse

A 2.5 kg dodgeball hits the back wall of a school gym at 15 m/s at an angle of 50º to the wall. The ball is in contact with the wall for 0.15s before bouncing back at 12 m/s at an angle of 60º to the wall. What average force was exerted by the ball on the wall?

Linear Momentum and Impulse

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Linear Momentum and Impulse

Linear Momentum

Impulse

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Linear Momentum and Impulse

Linear Momentum

Impulse

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Example: Impulse to a Soccer Ball

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Extra Practice