Intro to Physics
2nd Semester Topics
Momentum and Law of Conservation
of Momentum
8.1 Momentum
A truck rolling down a hill has more momentum than a roller skate
with the same speed. But if the truck is at rest and the roller skate
moves, then the skate has more momentum.
A small-massed
object with a large
speed can have the same momentum
as a large-massed object with a small
speed.
8.1 Momentum
Momentum is affected by the mass of
the object and its velocity (or speed).
Momentum is mass in motion!
8.5 Law of Conservation and Collisions
Motion of the cue ball
Motion of the other balls
Whenever objects collide in the absence of external
forces, the net momentum of the objects before the
collision equals the net momentum of the objects
after the collision.
8.4 Conservation of Momentum
The momentum before firing is zero. After firing, the net
momentum is still zero because the momentum of the
cannon is equal and opposite to the momentum of the
cannonball.
Velocity cannon to left is negative
Velocity of cannonball to right is
positive
(momentums cancel each other out!)
Impulse
Momentum and impulse
• Momentum is mass in motion (p = mv)
• An impulse transfers momentum (I = Ft).
• Impulse remains the same, but time of transfer and
impact force will vary inversely.
Same momentum, same impulse
More time, less force
Less time, more force
• Impulse = change in momentum
Ft = ∆mv
Collisions
8.5 Examples of Elastic Collisions when the objects
have identical masses
a.
A moving ball strikes a ball at rest.
Momentum of the first ball
was transferred to the
second; velocity is
identical
8.5 Inelastic Collisions
Start with less mass, end up with
more mass
Notice how speed changes to
conserve momentum (more mass,
less speed—inverse relationship!)
Example of an elastic collision with
objects same speed but different
masses
What happens to the speed of the smaller car after the elastic collision with
the more massive truck?
(the car’s speed increases to conserve
momentum)
Notice that the car has a positive velocity and the truck a negative velocity.
What is the total momentum in this system? (40,000 kg x m/s)
Work vs. Power
9.1 Work
Work = force × distance
•Did the weightlifter do work on the
barbell and weights?
•How?
•Is the weightlifter currently doing work
on the barbell and weights?
Why or why not?
•Explain two ways that the work done by
the weightlifter be increased.
1) Increase the weight on the ends
of the barbell
2) Increase the distance over
which the weightlifter pushes
the barbell and weights.
9.1 Work
Work has the same units as energy
Joules
Newton x meter
J
Nxm
•One joule (J) of work is done when a
force of 1 N is exerted over a distance of
1 m (lifting an apple over your head).
9.2 Power
P = w/t
Power is the rate at which work is done.
The unit of power is the joule per second, also known as the
watt.
One watt (W) of power is expended when one joule of work
is done in one second.
One kilowatt (kW) equals 1000 watts.
One megawatt (MW) equals one million watts.
Power
100 W incandescent
light bulb
How much electrical
energy per second?
100 joules per
second.
9.2 Power
Jet engine vs. lawn mower engine
Both receive ½ gallon of fuel (same energy, same work)
•A high-power jet engine does work rapidly, uses ½ gallon in 1 second.
•The low-powered lawn mower engine does work slowly, using ½ gallon in
30 minutes.
vs.
KE vs. PE
• KE
• Energy of motion
• PE
• Energy of position or
stored energy
9.5 Kinetic Energy
If an object is moving, then it is capable of doing work. It has
energy of motion, or kinetic energy (KE).
• The kinetic energy of an object depends on the mass of
the object as well as its speed.
Kinetic Energy
KE increases
with speed
9.4 Potential Energy
Gravitational Potential Energy
•Energy is stored in an object as the result of increasing its height.
•Work is required to elevate objects against Earth’s gravity.
•Example: Water in an elevated reservoir and the raised ram of a
pile driver have gravitational potential energy.
9.4 Potential Energy
Elastic Potential Energy—potential to do work
•Energy stored in a stretched or compressed spring or material.
•When a bow is drawn back, energy is stored and the bow can do
work on the arrow.
•These types of potential energy are elastic potential energy.
CHEMICAL POTENTIAL ENERGY
• Energy due to the bond position between
molecules (stored during bonding).
• Potential chemical energy is released from
chemical reactions (burning, for example).
• Fuels, Food, Batteries, for example.
Law of conservation of Energy
9.7 Conservation of Energy
When the woman leaps from the burning
building, the sum of her PE and KE
remains constant at each successive
position all the way down to the ground.
9.7 Conservation of Energy
Same energy
transformation applies
The 2 J of heat can be called nonuseful work (work that is not part of the
object’s total mechanical energy).
10 J of PE does 8 J
useful work on the
arrow and 2 J of
non-useful work on
the molecules that
compose the bow
and string and
arrow. The arrow
has 8 J of KE.
9.7 Conservation of Energy
Everywhere along the path of the pendulum bob, the sum of PE and
KE is the same. Because of the work done against friction, this
energy will eventually be transformed into heat.
Non-useful work can also be called non-useful energy!
Watch how KE and gravitational PE
transform
Where is the KE at the maximum?
Where is the PE at the maximum?
How is PE stored?
Watch the change in height vs. the change
in speed!
How does the change in height affect KE and PE?
What happens to KE and TME when the brakes
are applied? What work is being done?
Watch the transfer of KE and PE.
What happens to the PE when the skier moves down the hill?
What happens to the KE and TME when the skier travels over the
unpacked snow?
What work is done?
Same work, more force, less
displacement (from left to right)
Simple Machines and Mechanical
Advantage
• Mechanical advantage
• Same work, but
measures how many
different mechanical
times your input force is
advantage, input force
multiplied
and input distance
• This makes work easier, • No machine is 100%
but does not reduce the
efficient because of
amount of work done.
friction
• Which lever would have the highest
mechanical advantage?
c
b
a
Simple Machines
• Two families
Lever
Inclined plane
--Lever
--Ramp
--Pulley
--Wedge
--Wheel
and axle
--Screw
Pulley
Fixed pulley
1 support rope
MA = 1
Pulleys
MA = 2
Two supporting ropes
Pulleys
MA = ?
2
Pulley
How many support ropes?
4
What is the mechanical
advantage?
4
Wheel and Axle
• Wheel connected to a shaft
Thermal Energy
• Thermal energy is the energy of the molecules
that compose matter (they are in motion)
• Kinetic Theory
– All matter is made of molecules that move
randomly
– The faster the molecules move, the greater the
average kinetic energy of the molecules
– The higher the average kinetic energy, the higher
the temperature
Matter is
changing
state
solid
melting
freezing
liquid
evaporation
condensation
gas
Particle speed is
increasing
Increasing
Avg. KE
Increasing
Temp.
21.2 Heat
1. Heat is the quantity of thermal energy transferred
2. Heat always flows from a substance with a higher
temperature to a substance with a lower temperature.
3. Heat flows only when there is a difference in
temperature.
4. Heat units are calories or joules.
Heat and Heat flow
21.2 Heat
What causes heat to flow?
A difference in temperature
between objects in thermal contact.
Energy flow and phase change
23.8 Energy and Changes of Phase
If you heat a solid sufficiently, it will melt and become a liquid.
If you heat the liquid, it will vaporize and become a gas.
The change in the internal energy of a substance causes the change
of phase.
Three ways thermal energy is
transferred
22.1 Conduction
Heat from the flame causes atoms and free electrons in the end of the
metal to move faster and jostle against others. The energy of vibrating
atoms increases along the length of the rod.
22.2 Convection
Convection occurs in all fluids.
a.
Convection currents transfer heat in air.
b.
Convection currents transfer heat in
liquid.
22.3 Radiation
Most of the heat from a fireplace goes up the chimney by convection. The heat that
warms us comes to us by radiation.
Specific Heat Capacity
21.6 Specific Heat Capacity
A substance with a high specific heat capacity
can absorb a large quantity of heat before it
will raise in temperature (water has a high
specific heat).
A substance with a low specific heat requires
relatively little heat to raise its temperature
(copper has a low specific heat).
21.6 Specific Heat Capacity
highest
lowest
Generation of Sea Breezes
Day
Convection
Air above the
land heats
more rapidly
and rises
Sea breeze
Land
• low specific heat
• heat and cools rapidly
• less resistant to temperature change
Air above the
sea remains
cooler and
moves on
land to
replace the
land air that
rose
Sea
• high specific heat
• heats and cools slowly
• more resistant to temperature change
Generation of Sea Breezes
Night
Air above the
ground is
cooler than
the air above
the water and
moves over
the sea to
replace the
sea air that
rose
Land Breeze
Land
• low specific heat
• heat and cools rapidly
• less resistant to temperature change
Air above the
water is
warmer than
the air above
the land and
rises
Sea
• high specific heat
• heats and cools slowly
• more resistant to temperature change