Post on 05-Jan-2016
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 velocity
p 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 p
t
Linear momentum, cont’d
How is this related to F = ma?
F
p
t
mv t
mv
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 kg
vi0 m/s
vf40 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.
p
beforep
after
ExampleExample 3.2
A 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
m11,000 kg
m21,500 kg
vf4 m/s
p
beforem
1v
1 1,000 kg v1
p
after m
1 m
2 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 kg
1,000 kg4 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