Momentum & Review:

Objectives:

1.    Define momentum.

2.    Calculate momentum.

3.    Explain the law of conservation of momentum.

Web Resources:

Notes:

Momentum

Inertia is the property of mass that resists change. Therefore, it is safe to say that as the mass of an object increases so does its inertia.  Weight is the measurement of resting inertia and momentum is the measure of inertia at a certain velocity.  We all know that at the same forward velocity it would be harder to stop a rolling car that a rolling bike.  Common sense tells us that the mass of the car makes it more difficult to stop.  Here are some simple rules for momentum..

• Momentum can be calculated by multiplying the mass of an object by its forward velocity. (mv = kg*m/s)
• Mass and velocity are both directly proportional to the momentum.
•         If you increase either mass or velocity, the momentum of the object increases proportionally.
•         If you double the mass or velocity you double the momentum.
•         If you halve the mass or velocity you halve the momentum

Impulse:

At constant velocity the momentum of an object remains constant but if that object comes in contact with another object there is a change in momentum (acceleration or deceleration) that is related to the time of contact.  This relationship is called impulse.

• impulse = F*Dt
• F*t = D(m * v )(momentum)

The way that the knowledge of impulse becomes useful is in the application of time.  The longer it takes to change the momentum, the less force is exerted on an object and vice-a-versa.

• F = (mv)/t

To understand this think about stopping a car.  If the breaks are applied gently, the momentum of the car is changed gradually over a long period of time and the force on you the passenger is slight.  If you STOMP on the breaks, the momentum of the car changes immediately and the force on the passenger is great. The impulse is the same for the two situations but the time and force are different.

F t = F t

• Small force = long time
• large force = short time

(www.netcar.co.il/img2/milon/ 50%20Crash%20test%20s.jpg)

As you can imagine, the force of this crash was large because the time involved in the momentum change was very short.

Look at this example: Bungee jump (www.romansempire.com/jump.jpg)

The jumper had the same impulse force as he would have had if he hit the ground without the bungee.  The difference is that he extended the time of his momentum change thus decreasing the force of the impulse.

Bouncing is a way to increase impulse.  Because an object that bounces changes directions the force of impulse must be absorbed then generated by the target object.  (Impulse is nearly doubled.)

Conservation of Momentum:

In the absence of an external force, the momentum of a system remains unchanged.  What this means is that as objects come in contact with each other, momentum is transferred from one item to the next without a net gain or loss in momentum.

momentum before collision = momentum after collision

• Conservation of momentum follows Newton's 3rd law of action / reaction
• The size and direction of the impulse on the two items will be equal and opposite
• The net change in momentum = 0
• Assumes no friction
Collisions:

Elastic collisions

• Momentum is transferred from one object to the next
• Objects are not deformed in the collision
• The collision does not generate heat

(www.petersbilliards.com/ pics/break.jpg)

In the above picture.  The momentum from the cue ball is transferred to the remaining balls in the rack.  There is no net gain or loss in the elastic collision.

Inelastic collisions

• Colliding objects become entangled or deformed in the collision
• Collision may generate heat
• There is no net gain or loss in momentum, momentum must be recalculated based on the new combined masses of the entangled objects

(solomon.physics.sc.edu/.../explain/ images/inelastic7.jpg)

Assuming that the masses of the two cars are equal, the velocity of the combined system should be half.