Download Chapter 3: Conservation Laws

Chapter 3: Conservation
Laws
Interviewer: “So did you see which
train crashed into which train first?”
15-year-old: “No, they both ran into
each other at the same time.”
–BBC Radio 4
2
3.1 Newton’s Third Law and
Momentum
• Use Newton’s third law to explain various
situations.
• Explain the relationship between Newton’s
third law and momentum conservation.
• Solve recoil problems.
3
Newton’s Third Law
• “For every action, there is an equal and opposite
reaction.”
• Forces come in pairs. Bodies always exert equal
forces on each other, but that doesn’t mean the
acceleration is the same; acceleration also depends
on mass.
4
Newton’s Third Law
• “For every action force,
there is a reaction force
equal in strength and
opposite in direction” –
page 59 in your textbook.
• Unlike Newton’s 1st and 2nd
laws, which focus on one
object, the 3rd law involves
the mutual interaction
between two objects.
Does the moon
exert just as much
force on the earth
as the earth does
on the moon?
5
Balanced Forces
• Be careful, balanced forces
acting on a single object is
not an example of Newton’s
3rd law!
• Fnet = ma = 0
• Therefore, Normal equals
Weight (mg)
• Not because of Newton’s 3rd
Law!
• Both these forces act on the
same object, the book!
6
Action – Reaction Pairs
Force of table on
book, “Normal”
Force of earth
of book, W=mg
Force of book on
table
Force of book
on earth
Remember that the two forces in an
action-reaction pair never act on the
same object!
7
8
Momentum
• Remember the inertia of an
object indicated the object’s
resistance to change, but
both skaters have the same
mass, and same inertia.
• So which skater will be
harder to stop, both have
the same inertia, but
different momentum.
9
Momentum
• Momentum is a vector
so direction matters!
• Why doesn’t a massive
object at rest have
momentum?
10
Impulse
• An “impulse” is given to
an object, for example
the tennis ball, when a
force acts on the object
over a time interval.
• Impulse = Force * time
11
Impulse-Momentum Theorem
If an impulse is given to an object,
that impulse will change the object’s
momentum!
12
Conservation of Momentum
•
•
•
Two objects (boy and ball) each
exert equal forces on each other as
the boy throws the ball. The two
objects will be in contact for the
same amount of time. Therefore the
impulses on each object will be the
same (but in opposite directions).
If the impulse on each object is the
same, so is the change in
momentum (again in an opposite
direction).
If interacting objects in a system are
not acted on by outside forces, the
total amount of momentum in the
system cannot change.
mAvA1  mBvB1  mAvA2  mBvB 2
13
14
Class Problems
• An astronaut floating in space throws a
2 kg hammer to the left at 15 m/sec. If
the astronaut’s mass is 60 kg, how fast
does the astronaut move to the right
after throwing the hammer?
mAvA1  mBvB1  mAvA2  mBvB 2
• A group of playful astronauts, each with
a bag full of balls, form a circle in outer
space. Describe what happens when
they begin tossing balls simultaneously
to one another.
15
3.2 Energy and Its Conservation
•
•
•
•
Describe work and energy.
Calculate potential energy.
Calculate kinetic energy.
Apply the law of conservation of energy to
explain the motion of an object acted on by
gravity.
16
What is Energy?
• We have talked about
energy many times, page 65
is a good summary.
• Energy is a quantity that
measures the ability to
cause change in a physical
system.
• The metric unit for energy is
named after the English
physicist James Joule
(1818–1889).
17
What is Work?
• We say work is done on an object when a force acts
to move that object in the direction of the force.
• Work done on an object transfers energy to that
object.
• An object (or system) with energy has the ability to
do work.
• Work is also measured in Joules (J).
18
Force and Distance
• The work done on an object can be positive or
negative: positive if it adds energy to the object,
negative if the object loses energy!
• Forces acting 90o to the motion do not do work.
• Remember W = F*d, so if there is no motion
(distance) no work is done.
Force is at 90o to distance => no work
box moving to the right
No distance => no work
Negative work done –
Box loses energy!
Positive work done – energy is
added to the box
19
Potential Energy
• Potential energy is energy
due to the position of an
object in a system.
• An object some height
above the ground has
potential energy due to
the earth’s gravity.
• There are other forms of
potential energy such as
elastic and electrical.
20
Kinetic Energy
• Energy of motion is called
kinetic energy.
• Kinetic energy depends on
both an object’s speed
and its mass.
– Double the mass of a
moving object and the KE
will double.
– Double the speed and
the KE will quadruple,
since KE ~ v2.
21
Class Problems
• Work: You are on the track team working out
by pushing a “sled” with a force of 50 lbs (F =
2250 N) half a football field (d = 50 m), how
much work do you do?
• Potential Energy: How much do you have on
the roller coaster shown if you and the coaster
have a combined mass of 80 kg and are 4
meters off the ground?
• Kinetic Energy: How much kinetic energy does
a bullet of mass = 40 grams moving at 300 m/s
have?
22
Law of Conservation of Energy
• An important conservation
law in physics: “Energy can
never be created or destroyed,
just converted from one form
into another.”
• The diver initially has useful
PE which converts to KE on
the way down. Ultimately the
energy turns into useless heat
energy, but the total energy
for the “system” in constant.
23
Conservation of Energy Problems
• We can use the idea of
conservation of energy to solve
problems.
• Consider the diagram to the right:
first you might have to use a winch
to do work lifting the block… now
complete the description…
• We could find the speed (velocity)
of the block right as it hits the stake
using conservation of energy!
24
Conservation of Energy Problems
• Remember in Chapter 2 we solved
free fall problems. Can you recall how
to find the maximum height if the
initial velocity is 40 m/s?
• How many seconds does it take to get
to the highest point?
• What’s the average velocity?
• What the distance (or height)?
• We could also use conservation of
energy to solve for h.
1 mv2  mgh
2
25
“Using” vs. “Conserving” Energy
• You turn on a light in your
study, assume the energy
ultimately came for a
hydroelectric power plant.
Describe the what is going
on…
• In what sense do you use
energy up?
• Is energy really destroyed?
• What is being used up?
Energy can never be created or
destroyed, just converted
from one form into another
26
Conservation of Mechanical Energy
Mechanical Energy = Kinetic Energy + Potential Energy
27
3.3 Collisions
• Distinguish between elastic and inelastic
collisions.
• Use momentum conservation to solve
collision problems.
• Explain how momentum, impulse, force, and
time are related.
28
Elastic and Inelastic Collisions
• A collision occurs when two or
more objects hit each other.
• When a perfectly elastic
collision occurs, objects bounce
off each other with no loss in
the total kinetic energy.
• In an inelastic collision, objects
change shape or stick together,
and the total kinetic energy of
the system decreases.
• During any collision, momentum
is always conserved.
29
One Dimensional Collision
• When two (or more) objects
collide, momentum is
conserved. But for the
system of objects, not for any
one individual object.
• That is the total momentum
before equals the total
momentum after the
collision.
• m1v1 + m2v2 = m1v1 + m2v2
30
Trains “Coupling” after Collision
• Both trains share a common final velocity!
• m1v1 + m2v2 = (m1 + m2)v
31
Momentum as a Vector
When the firecracker bursts, the vector sum of the
momenta of its fragments add up to the firecracker’s
momentum just before bursting.
32
Forces in Collisions & Bouncing
• The impulse equals the change in
momentum, so…
• …the bigger the change in
momentum, the greater the
impulse and force…
• Changing directions usually means
a bigger change in momentum!
A “Pelton Wheel” has curved paddles
instead of flat ones – causing the water
to “bounce” away creating more force!
http://www.youtube.com/watch?v=3eE9NVKCipQ
33
Both cars have the same momentum to begin with – and both have the
same momentum at the end (zero!) – so the change in momentum is the
same, and therefore the impulse on the cars is the same….
But would you rather stop with a large force in a short time, or with a
smaller force over a longer time interval?
34
Car Crash Safety
• Remember the impulse on an
object equals its change in
momentum.
• But for a given impulse, you can
decrease the force by increasing
the time! Seat belts and air
bags both help extend time.
35
Class Problems
• A 75 kg crash dummy traveling at 22 m/s
(~50 mph) stops in 0.01 seconds. What is
the force on the driver? What is the
acceleration? How could we increase the
time to lessen the force and acceleration?
What if the time to stop was 0.15 seconds?
• An 8,000-kg train car moves to the right at
10 m/sec. It collides with a 2,000-kg parked
train car. The cars get stuck together and roll
along the track. How fast do they move
after the collision?
36
Rockets: Out of This World Travel
Robert H. Goddard (1882 – 1945)
New York Times editorial:
"Professor Goddard . . . does not
know the relation of action to
reaction, and of the need to
have something better than a
vacuum against which to react…
seems to lack the knowledge
ladled out daily in high schools."
July 1969 - Further investigation and experimentation
have confirmed the findings of Isaac Newton in the 17th
Century and it is now definitely established that a rocket
can function in a vacuum as well as in an atmosphere.
The Times regrets the error.
37
Rockets: Out of This World Travel
• Think back to Newton’s 3rd Law!
• Momentum is conserved so
that the momentum of the
rocket equals the momentum of
the gas.
• Remember momentum is a
vector!
The two ice skaters have zero momentum initially, after
pushing off of each other one acquires momentum to the
right, the other the same amount of momentum to the left?
Who has the greater velocity?
38
Chapter 3 Review
1)
2)
3)
4)
5)
6)
When swimming, you push the water backwards – call this action. What is the
reaction force?
(a) Which has the greater mass, a heavy truck at rest or a rolling skateboard? (b)
Which has a greater momentum?
Does impulse equal momentum, or a change in momentum?
You can’t throw a raw egg against a wall without breaking it, but you can throw it
at the same speed into a sagging sheet without breaking it.
Comic-strip hero Superman meets an asteroid in outer space and hurls it at 100
m/s, as fast as a bullet. The asteroid is a thousand times more massive than
Superman. In the strip, Superman is seen at rest after the throw. Taking physics
into account, what would be his recoil speed?
Most Earth satellites follow an oval shaped (elliptical) path rather than a circular
path around the Earth. The PE increases when the satellite moves farther from
the Earth. According to the law of energy conservation, does a satellite have its
greatest speed when it is closest to or farthest from Earth?
39