#### Transcript Conservation of Energy

```Conservation of Energy
Work
•
To do work on an object you need an
application of a force AND movement
due to the force.

•
Example: Lifting a barbell. A force is applied
to the barbell and the barbell moves in the
direction of the force
If there is no movement, there is NO
work being done on an object.
Work: force times displacement; when
a force is applied at a constant velocity
in the same direction.
 The movement must be along the same plane
as the force applied.
 Units: Joule (J)
 Equation:
W = Fd
• W = Work (J)
• F = Force (N)
• d = Distance (m)
A man holds a 50 lbs box in the air. Is he
doing any work?
No. Even though his muscles are getting
tired, according to physics he is not doing
any work because there is no
displacement of the box. No movement
means no work.
Work, Force and Displacement
•
•
Work is directly proportional to force
(displacement stays the same).
2F = 2W
½F = ½W
Work is directly proportional to
displacement (force stays the same).
2d = 2W
½d = ½W
Work is done lifting a barbell. How much
more work is done lifting a twice as
heavy barbell the same distance?
Twice as much work. Force and work are
directly proportional, so if you double
force then you double the work.
W=Fd
2W = 2F d
How much work is done lifting a twice as
heavy barbell twice as far?
Four times as much work
W=Fd
4W = 2F 2d
In this case, both the force and the
distance were doubled thereby causing
four times as much work to be done.
An object is accelerating for 5 meters. If
a force of 30 N is being applied to the
object, what is the work done on the
object?
W= ?
F = 30 N
d=5m
W = Fd
W = (30 N)(5m) = 150 J
Power
• The quantity work has to do with a force
causing a displacement. Work has nothing
to do with the amount of time that this force
acts to cause the displacement.
• Power describes how quickly work gets
done.
Power: the rate at which work is
done.
 The less time it takes for work to be done, the
greater the power.
 Unit: Watt (W)
 Equation:
P=W/t
• P = Power (Watts)
• W = Work (Joules)
• t = time (seconds)
Power, Work, and Time
• Power is directly proportional to work
2W = 2P
½W = ½P
• Power is inversely proportional to time
2t = ½P
½t = 2P
Two physics students, Will N. Andable and Ben
Pumpiniron, are in the weightlifting room. Will
lifts the 100-pound barbell over his head 10
times in one minute; Ben lifts the 100-pound
barbell over his head 10 times in 10 seconds.
Which did the most work? Which student
delivers the most power? Explain.
 Both did the same amount of
work (Fd). Ben did his
work more quickly,
so he used more power.
Identical twins are late to class. One twin runs
up the stairs while the other twin walks up
the stairs. Which twin did more work?
 Both twins applied the same force over the same
distance. The twins did the same amount of
work.
Which twin used more power?
 Both twins did the same amount of work;
however, the twin that ran did the work more
quickly and therefore used more power.
If an object has a work of 20 J exerted on
it for a time of 4 seconds, what is the
power?
P = ?
W = 20 J
t=4s
P = W/t
P = 20 J/4s = 5 Watts
Mechanical Energy
• Mechanical energy can be either kinetic
energy (energy of motion) or potential
energy (stored energy of position).
Mechanical energy: the energy
which is possessed by an object due to
its motion or its stored energy of
position
 Mechanical energy is the ability to do work
 SI Unit: Joule (J)
 Ex: KE and PE
Potential Energy
Potential energy: stored energy due
to position.
 PE has the potential to do work
 SI Unit: Joule (J)
 Ex: Elastic and Gravitational Potential
Energy
Gravitational Potential Energy
Gravitational potential energy:
energy that is stored in an object due
to its height


An object has the potential to fall
SI Unit: Joule (J)

Equation: PEG = mgh
• PEG = Gravitational PE (J)
• M = mass (kg)
• G = acceleration due to gravity (10m/s2)
• H = height (m)
If a ball with a mass of 2 kg is raised to a
height of 10 m, what is the gravitational
PE of the ball?
PEG = ?
m = 2 kg
g = 10 m/s2
h = 10 m
PEG = mgh
PEG = (2 kg)(10 m/s2)(10 m) = 200 J
Elastic Potential Energy
Elastic Potential Energy: the potential
energy stored in an elastic object due
to change in shape.
 Elastic PE exists in objects that can be
stretched and will return to their original shape
 SI Unit: Joule (J)
 Ex: rubber bands, springs
Does a car hoisted for lubrication in a service
station have elastic or gravitational PE?
 Gravitational
How much more work will raise the car twice
as high?
 Twice as much work
How much more potential energy will it have
then?
 Twice as much potential energy
Which type of potential energy does a
bow stretched to shoot an arrow have?
Both elastic and gravitational PE. It has
elastic because it is stretched and has the
potential to move back to its original
position, and it has gravitational because it
is at a height and has the potential to fall.
Work and PE
• The amount of PE an object has is equal to the
work done to raise the object a vertical distance.
• The object has the potential to do work.
• The same amount of work was done in the picture
below because all the balls are at the same vertical
height. All the balls have the same PE
Kinetic Energy
Kinetic energy: energy of an object in
motion
 An object MUST be moving to have KE
 An object with KE also has momentum
 SI Unit: Joule (J)
 Equation: KE
= ½mv2
• KE = Kinetic energy (J)
• m = mass (kg)
• v = velocity (m/s)
How much kinetic energy does a 1 kg
cart have moving at 1 m/s?
KE = ?
m = 1 kg
v = 1 m/s
KE = ½mv2
KE = ½(1)(12) = ½ Joule
KE, Mass & Velocity
• KE is directly proportional to mass
2m = 2KE
½m = ½KE
• KE is directly proportional to velocity
squared
2v = 22KE = 4KE
3v = 32KE = 9KE
4v = 42KE = 16KE
Work and KE
• An object that is changing its KE is
changing:
 Its mass
 Its velocity
 Both mass and velocity
• If an object is changing its velocity, it is
accelerating, so a force is applied to it
 So there is work done on it
 A change in KE means work is done by the
object
KE and Stopping Distance
• KE is equal to the amount of work required
to increase the speed of a moving object
or the work the object can do while being
brought to rest.
• Consider a car that doubles its speed.
 2v = 22KE = 4KE.
 If 4KE, then 4W.
 So an object moving TWICE as fast takes
FOUR times as much work to stop. If this car
were to skid, it would travel FOUR times as
far.
You are traveling behind a truck on the
highway. Knowing that you need to
leave 100 ft when traveling at 30 mph to
stop, you figure that you can leave 200
ft between you and the next car if you
are going 60 mph…in case you need to
suddenly stop. The truck in front of
you suddenly stops to avoid an
accident. You slam on the breaks to
avoid hitting the truck, but you still
plow into it anyway. Why?
had not just double the KE, but 4 times as
much KE. Because of this, you actually
needed not just double the stopping
distance, but 4 times the stopping
distance.
Work-Energy Theorem
Work-energy theorem: whenever work is
done, the energy of a system changes.
 If you change the PE, you are doing work
 If you change the KE, you are doing work
 Ex: An object that changes it KE is moving,
thus doing work. An object being lifted or
stretched to gain PE is having work done on
it.
 Equations:
W = ΔKE; W= -ΔPE
• Remember, both work and energy are
measured in Joules
• Movement must have taken place for a
change in energy, and therefore work, to
have taken place.
Does a car slowing down on a rough surface
have work being done on it?
 Yes! The car is slowing down, so it is changing
its KE. A change in KE results in work being
done on the car by the road
Does a student sitting at the top of the stairs
have work being done on them?
 No! They are not moving so they are not
changing their KE or PE, so no work is being
done.
The Law of Conservation of Energy
Law of Conservation of Energy: energy
cannot be created or destroyed but can
change forms
 Energy changes from one form to another
 Ex: PE changes to KE at the bottom of a hill
 Equation: ME = PE + KE
ME before = ME after
(PE + KE)before = (PE + KE)after
• The total ME (mechanical energy) remains
the same throughout a system.
 It’s just a matter of how much is KE and how
much is PE
 Ex: At the top of a pendulum swing, there are
50 J of PE; there is no KE b/c it is not moving.
At the bottom of the swing, all the PE has
converted to all KE. So the KE is 50 J and the
PE is 0 J. In the middle of the swing, it would
be 25 J of PE and 25 J of KE.
At the very top of a roller coaster, a girl
has a potential energy of 100 J. What
would be her kinetic energy at the very
bottom of the hill (assuming there is no
energy lost to air resistance)?
100 J. Since energy is neither created nor
destroyed, all the potential energy at the
top of the roller coaster will be converted
into all kinetic energy.