Transcript Energy

Energy
Chapter 5
What is energy?
The property of an object that allows it to
produce a change in itself or its
environment.
 In this class we will study
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Work
 Gravitational Potential Energy
 Kinetic Energy
 Spring Potential Energy
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Work
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Generic term for energy given to an object from
an outside source or energy lost to the outside
from an object.
W=Fdcosθ
θ is the angle between the force and the
displacement.
Unless explicitly told otherwise, assume that the
angle between force and displacement is 0.
When θ=90o, cosθ=0 so no work is done.
Work
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Unit for energy is the Joule.
Other units: calories, kilowatt hours,
Negative work means that the object in question
is losing energy i.e. friction.
Sometimes labeled Q when referring to heat
specifically.
kgm
kgm2
J  Nm  2 (m)  2
s
s
Practice Problems
A man lifts a 150kg barbell up 2.5m. How
much work does he do?
 A woman pushes a penguin up an incline
of angle 32 degrees. If she pushes
horizontally and does 5000J of work, the
penguin moves 10m. How much force
does she exert?
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Power
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The rate at which energy is transferred.
W Change in Energy
P

t
t
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Unit is a Watt
1W=1J/s, so 1J=1Ws and we can convert from
Joules to kWhr.
English unit is horsepower.
Power Problem
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You leave the 65W bulb in your room on for two
weeks. How much energy does it use?
If the electric company charges 12.5 cents per
kilowatt hour, how much does it cost your
parents?
Mechanical Energy
Energy due to movement or position.
 Kinetic energy-energy of motion
 Potential energy-energy due to position or
shape of an object.
 Total energy-the sum of all potential and
kinetic energies of an object or system.
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Kinetic Energy
2
1
KE 
mv
2
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Depends on velocity and mass
Doubling velocity quadruples the energy
If a bird flying at 5m/s has a kinetic energy of
1.4J, what is the mass of the bird?
What is the difference in kinetic energy between
a 2000kg car moving at 5mph,10mph, and
15mph.
Work Kinetic Energy Theorem
W  KE
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A car accelerates on a frictionless road at a rate
of 3.6m/s2. If the car has a final velocity of
42m/s and accelerates over 192m, what was its
initial velocity?
Gravitational Potential Energy
PE  mgh
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H is subjective
Only really measures changes in PE
Can be negative whereas KE cannot
What is the potential energy of a roller coaster car of
mass 450kg that is 17m off of the ground?
A 45kg diver dives off of a board which is 7m above the
bottom of the pool. If the pool is 2m deep, what is the
change in potential energy of the diver from when she is
on the board to when she hits the surface of the water?
Conservation of Energy
In a closed system, energy cannot be
created or destroyed, only changed from
one form to another.
 Closed system
 Calculate total energy before and after and
set them equal to each other.
 Energy added to a system is work on the
initial side, energy lost by the system is
work on the final side.
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Practice
A rock is dropped off of a 100m high cliff.
How fast is it going right before it hits the
ground?
 A rock is thrown off of a cliff at an angle of
37 degrees above the horizontal at a
speed of 21m/s. If it is going 43m/s when
it hits a 2.5m tall man in the head, how
high is the cliff?
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Friction
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Takes energy from the system and wastes it in
heat.
It exerts a force over a distance so:
W fr  F fr d
Practice
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A 6kg tuna salad sandwich starts from rest and
slides down a 20 degree incline that is 4m high.
If the final velocity of the box is 7m/s what is the
work done by friction? What is the magnitude of
the frictional force?
A 10kg wagon full of bananas, starting from rest,
is pulled with horizontally with a 25N force
across level ground. If the coefficient of friction
between the wagon and the ground is 0.2, how
quickly is the wagon moving after 25m?
Additional Problems
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If the 2kg ball above starts with an initial velocity of
6.7m/s at 2m but only rolls up to a height of 3.1m, how
much work is done by friction?
A driver has a truck full of chickens. The chickens and
truck have a combined mass of 2200kg. As the truck
driver coasts down a frictionless hill, 300kg of the
chickens fly out of the truck. If the hill is 11m high and
his initial velocity is 12m/s, how fast is he going at the
bottom of the hill?
Springs
Springs
PEs 
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1
2
2
kx
x=How much the spring is streched or
compressed from its equilibrium position.
Measured in meters.
k=Spring constant, a measure of how stiff the
spring is. The stiffer the spring, the higher the k.
Measured in N/m
Practice Problems
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A spring attached to a 2kg block is stretched
horizontally 12cm from its equilibrium position. If
the block is traveling at 0.89m/s when the spring
gets back to its equilibrium position, what is the
spring constant of the spring?
A bungee jumper jumps off of a bridge at a
speed of 2m/s. The bungee cord has a spring
constant of 32N/m and is 12m long when
unstreched. If the jumper falls a distance of 45m
before switching directions, what is her mass?