Vern J. OstdiekDonald J. Bord

Chapter 3Energy and Conservation

Laws

Conservation laws

The most fundamental ideas we have in physics are conservation laws. Statements telling us that some quantity

does not change Conservation of mass states:

The total mass of an isolated system is constant.

To apply these, we must define a “system.”

Conservation laws, cont’d

A system is just a collection of objects we decide to treat at one time. The tanker and fighter can represent a

system. The fuel leaving

the tanker goes into the fighter:mass is conserved

Linear momentum

Linear momentum is defined as the product of an object’s mass and its velocity.

We typically just say momentum.

linear momentum mass velocityp mv

Linear momentum, cont’d

Momentum is a measure of an object’s state of motion. Consider an object whose momentum is

1 kg·m/s This could be a 0.005 kg bullet traveling at 200

m/s. This could be a 0.06 kg tennis ball traveling at

16.7 m/s.

Linear momentum, cont’d

Momentum (continued)

high mass or high velocity high momentum

high mass and high velocity higher momentum

low mass or low velocity low momentum

low mass and low velocity lower momentum

Linear momentum, cont’d

Newton’s 2nd law is closely related to momentum. The net external force acting on an object

equals the rate of change of linear momentum:

force change in momentum

change in time

F pt

Linear momentum, cont’d

How is this related to F = ma?

F

pt

mv

tm v

tma

ExampleExample 3.1

Let’s estimate the average force on a tennis ball as it is served. The ball’s mass is 0.06 kg and it leaves the racquet with a speed of 40 m/s. High-speed photography indicates that the contact time is about 5 milliseconds.

ANSWER:The problem gives us:

The force is:

ExampleExample 3.1

m 0.06 kgvi 0 m/s

v f 40 m/s

t 0.005 s

F mv

t

0.06 kg 40 m/s 0.005 s

480 N 108 lb

Linear momentum, cont’d

This tells why we must exert a force to stop an object or get it to move. To stop a moving object, we have to bring its

momentum to zero. To start moving an object, we have to impart

some momentum to it.

Momentum

When the speed of an object is doubled, its momentum:

A. remains unchanged in accord with the conservation of momentum.

B. doubles. C. quadruples. D. decreases.

Impulse

The change in momentum of an object is equal to the impulse applied to it (force multiplied by the time interval during which the force is applied).

Impulse =

The change of momentum, or the Force multiplied by time, is called “Impulse”.

p Ft

Impulse Impulse tells us that we can change the

momentum using various forces and time intervals.

You can get the same impulse by using a large force for a short time, or using a small force for a long time.

Impulse

Impulse• product of force and contact time• impulse = force time = Ft

great force for long time large impulsesame force for short time smaller impulse

Impulse

When the force that produces an impulse acts for twice as much time, the impulse is doubled as well.

Example:• golfer follows through while hitting the golf ball

Impulse

When a car is out of control, it is better to hit a haystack than a concrete wall. Common sense, but with a physics reason:

Same impulse occurs either way, but extension of hitting time reduces hitting force.

Conservation of momentum

The Law of Conservation of Momentum states:

The total momentum of an isolated system is constant (no external forces).

A system will have the same momentum both before and after any interaction occurs. When the momentum does not change, we say it is conserved.

Conservation of linear momentum, cont’d

This law helps us deal with collisions. If the system’s momentum can not change,

the momentum before the collision must equal that after the collision.

Conservation of linear momentum, cont’d

We can write this as:

To study a collision: Add the momenta of the objects before the

collision. Add the momenta after the collision. The two sums must be equal.

pbefore pafter

ExampleExample 3.2A 1,000 kg car (car 1) runs into the rear of a stopped

car (car 2) that has a mass of 1,500 kg. Immediately after the collision, the cars are hooked together and have a speed of 4 m/s. What was the speed of car 1 just before the collision?

ANSWER:The problem gives us:

The momentum before:

The momentum after:

ExampleExample 3.2

m1 1,000 kg

m2 1,500 kg

v f 4 m/s

pbefore m1v1 1,000 kg v1

pafter m1 m2 v2 2,500 kg 4 m/s

ANSWER:Conserving momentum

ExampleExample 3.2

1,000 kg v1 2,500 kg 4 m/s v1

2,500 kg1,000 kg

4 m/s 10 m/s

DISCUSSION:Both cars together have more mass than just

car 1.Since both move away at 4 m/s, the lighter car

1 must have a greater speed before the collision.

ExampleExample 3.2

Conservation of linear momentum, cont’d

How do rockets work? The exhaust exits the rocket

at high speed. We need high speed because

the gas has little mass. The rocket moves in the

opposite direction. Not as fast as the

gas because it has more mass