0.18 Phy1160: force and motion -- momentum, impulse, and conservation  (Page 3/14)

Proportional to both mass and velocity

From the above equation , it can be seen that an object can have a large momentum if either its mass or its velocity is large. Bothvariables are of equal importance in determining the momentum of an object.

A car and a tennis ball

Consider the case of a car and a tennis ball rolling down the street at the same speed. Because the car has greater mass, it has more momentum than thetennis ball. However, if the car stops and the tennis ball continues to roll, the tennis ball then has the greater momentum.

Momentum is zero at rest

The momentum of any object at rest is zero. Objects at rest do not have momentum because their mass is not in motion.

The quantity of momentum

The quantity of momentum possessed by an object depends on:

• How much mass is moving, and
• How fast the mass is moving.

For example, a small mass moving very fast can have the same momentum as a large mass moving slowly. You sometimes hear about the major damage that avery small piece of space junk moving at a very high speed could do if it were to strike the International Space Station.

A bullet shot from a firearm has a very small mass, but it has a very high velocity. Consequently, it probably has more momentum than a baseball pitchedfrom second base to home plate, even though the baseball has much more mass.

What happened to the dinosaurs?

Similarly, you may have heard that an asteroid with a mass that was small relative to the mass of the earth but with an extremely high velocity led to theextinction of the dinosaurs about 160 million years ago when it collided with the earth in the Gulf of Mexico.

Impulse

Momentum can be changed by a force

An object with momentum can be stopped if a force is applied against it for a given amount of time. For example, when a car approaches a red traffic light,the driver applies the brakes. The friction of the tires on the pavement applies a force to the car, which eventually reduces the car's velocity to zero. When thevelocity goes to zero, the momentum also goes to zero.

Therefore, the momentum of an object can be changed by applying a force to the object over a given period of time.

Unbalanced forces cause acceleration

As you learned in earlier modules, an unbalanced force always accelerates an object, either causing the object to speed up or causing the object to slowdown. Either way, the application of an unbalanced force to an object will change the velocity of the object. When the velocity of the object is changed, the momentumof the object is changed as well.

The impulse

Let's use what we know from Newton's second law to derive a concept known as impulse .

The product of mass and acceleration

You learned in an earlier module that force is equal to the product of mass and acceleration:

F = m * a

where

• F represents Force
• m represents mass
• a represents acceleration

The rate of change of velocity

You also learned that acceleration is the time rate of change of velocity, or

a = (v2 - v1)/t

where

• v2 - v1 indicates a change in velocity during a time interval given by t.