Download Energy and Power (Chapter 7)

ENERGY
PHY1121
This Week



We introduce the concept of ENERGY.
Last WebAssign before the exam is posted.
Read Chapter 7 “Energy”
Next Class Week (After Break)

Monday – We will spend the entire session working on problems for the
chapters we have covered since the last examination. (Send Requests)
 Chapters 6 and 7 in the textbook
 The Pythagorean Scale
 (Measured Tones – Pages 1-9)
 Class Notes
 Beats and Intervals (Also Review p289-291, 324-5 in textbook)
 Pressure (Text pages 214-218)
 Review all WebAssigns on these topics.

Enjoy your break!!!

Wednesday – EXAMINATION #2

Friday – Onward and Upward
There are many different kinds of energy ..
many listed in the papers recently.

Chemical (Burning coal, oil, wood)
Wind
Thermal
Nuclear
Energy of Motion
Energy related to position (Potential Energy)
Sound

This topic has been politicized during the last year.







We will avoid the politics. Maybe.
Let’s begin with the definition of WORK
F
Distance “d”

The man applies a constant force F.

He pushes the cart over a distance d.

The force is in the DIRECTION of the motion. (Important – later)

There is NO friction

The amount of work that he does is defined as

Work done = Force x Distance through which the force acts

W=F x d
Example – A man pushes a 100 kg cart with a
force of 50 N over a distance of 10 m. How
much work did he do?
Force  50 N
distance  10 m
Work  50N x 10 m  500 N - m
The units of work are Newton-Meters
also called a JOULE
Observation




When the pusher stops pushing the object, it
continues to move.
It therefore has acquired some energy of motion
from the work that the pusher did.
We call this energy of motion, KINETIC ENERGY
We define Kinetic Energy as
1 2
KE  mv
2
Notice … Push a mass m through a
distance “x” with a force F:
F  ma  v 2f  v02  2ax
v 2f  v02  2ax
F
v v  2 x
m
1
1
2
Fx  mv f  mv02
2
2
2
f
2
0
DEFINE KINETIC ENERGY
1 2
KE  mv
2
1
1
2
Fx  mv f  mv02
2
2
In the absence of friction, he work done by
an external force on a mass is
Equal to the change in its Kinetic Energy.
A First Equation
Energy of Motion

Like momentum, kinetic energy depends on the mass
and the motion of the object. But the kinetic energy
KE of an object has its own equation.
Details of the Equation
Energy of Motion


The factor of ½ makes the kinetic energy
compatible with other forms of energy, which we
will study later.
Notice that the kinetic energy of an object
increases with the square of its speed.

This means that if an object has twice the speed, it has
4× the kinetic energy; if it has 3× the speed, it has 9×
the kinetic energy; and so on.
Units of Energy
Energy of Motion

The units for kinetic energy, and therefore for all types of
energy, are kilograms multiplied by (meters per second)
squared (kg · m2/s2).


joule (J).
Kinetic energy differs from momentum in that it is not a
vector quantity.


This energy unit is called a
An object has the same kinetic energy regardless of its direction as
long as its speed does not change.
A typical textbook dropped from a height of 10
centimeters (about 4 inches) hits the floor with a kinetic
energy of about 1 J.
Doing the Math
Energy of Motion

The kinetic energy of a 70-kilogram (154-pound)
person running at a speed of 8 meters per second
is:
KE = ½mv 2
= ½(70 kg)(8 m/s)2
= (35 kg)(64 m2/s2) = 2240 J
Conservation of Kinetic Energy


The search for invariants of motion often involved
collisions. In fact, early in their development, the
concepts of momentum and kinetic energy were
often confused.
Things became much clearer when these two were
recognized as distinct quantities.
We have already seen that momentum is conserved
during collisions. Under certain, more restrictive
conditions, kinetic energy is also conserved.
 Remember, there are other forms of energy than kinetic
energy!

At the Moment of Impact
Conservation of Kinetic Energy

Consider the collision of a billiard ball with a hard
wall. Obviously, the kinetic energy of the ball is not
constant.
At the instant the ball reverses its direction, its speed is zero,
 and therefore its kinetic energy is zero.


As we will see, even if we include the kinetic energy
of the wall and Earth, the kinetic energy of the system
is not conserved.
Outcomes & Averages
Conservation of Kinetic Energy


However, if we don’t concern ourselves with the details of what happens
during the collision and look only at the kinetic energy before the
collision and after the collision, we find that the kinetic energy is nearly
conserved.
During the collision the ball and the wall distort, resulting in internal
frictional forces that reduce the kinetic energy slightly.


In this case the kinetic energy of the ball after it leaves the wall equals
its kinetic energy before it hit the wall.


Let’s assume we have “perfect” materials and can ignore these frictional
effects.
Collisions in which kinetic energy is conserved are known as elastic collisions.
Many atomic and subatomic collisions are perfectly elastic.
Final Notes
Conservation of Kinetic Energy

Collisions in which kinetic energy is lost are known as
inelastic collisions.



The loss in kinetic energy shows up as other forms of energy,
primarily in the form of heat, which we will discuss in Chapter 13.
Collisions in which the objects move away with a common
velocity are never elastic.
The outcomes of collisions are determined by the
conservation of momentum and the extent to which kinetic
energy is conserved.

We know that the collisions of billiard balls are not perfectly elastic
because we hear them collide. (Sound is a form of energy and
therefore carries off some of the energy.)
Is kinetic energy conserved here?
In the previous slide

All of the kinetic energy was lost.
 It
crunched the metal
 It created heat (thermal energy)
 It destroyed the tires

Momentum WAS conserved

Cars are not conserved!
A Better Statement of Conservation
of Energy
Kinetic
Energy
Before
Collision
Kinetic
Energy
After
Collision
Energy Lost
To Friction,
Etc.
More Better

There is still another form of “mechanical energy”
that we haven’t discussed yet.
 This

is called “potential energy”
If we include this form of energy, a “more better”
statement of conservation of energy would be:
 The
total mechanical energy BEFORE a collision (or
interaction) is equal to the total FINAL mechanical
energy after the collision + any losses to friction,
chemical explosions, etc.
 This can also work in reverse.
Forces That Do No Work

The meaning of work in physics is different from the common
usage of the word.


Commonly, people talk about “playing” when they throw a ball and
“working” when they study physics.
The physics definition of work is quite precise—work occurs
when the product of the force and the distance is nonzero.


When you throw a ball, you are actually doing work on the ball; its
kinetic energy is increased because you apply a force through a
distance.
Although you may move pages and pencils as you study physics, the
amount of work is quite small.
Pushing At An Angle
Forces That Do No Work

Often, a force is neither parallel nor perpendicular to the
displacement of an object. Because force is a vector, we can
think of it as having two components, one that is parallel and
one that is perpendicular to the motion as illustrated in Figure
7-4. The parallel component does work, but the perpendicular
one does not do any work.
Any force can be replaced by two perpendicular
component forces. Only the component along
the direction of motion does work on the box.
Mass held high and released ….
Mass held at some height.
Not moving.
No Kinetic Energy
Before it hits the ground it is now moving.
It has Kinetic Energy.
Where did it come from??
Originally, the mass was on the ground
(our reference level for y=0)
F
h
mg
Force
Required
To Raise item
to
Height “h”
The work done to raise
the block to the height h
is the
FORCE x Distance =(mg)x(h)
This is the amount of energy
That is stored by virtue of its
Position above the ground.
We call this the potential energy
PE = mgh
Another Example
Energy winds up
Stored in t he spring!
Some important points



When doing potential energy problems, always
identify the “zero” or reference position (height)
of energy.
Remember that Potential energy, Kinetic Energy
and all energies are SCALARS!
Momentum, of course, is a VECTOR.
The Pendulum
All Potential Energy
Reference Level
All Kinetic
Energy
Both types of
Energy
How Fast??



The wind turbine doesn’t
actually store energy.
It can only generate a
certain amount of energy
per minute (or hr or sec).
Therefore we can only use
this energy at a certain
rate (or, send it along the
grid for someone else to
use.
Power




In previous chapters we discussed how various quantities change with
time.

For example, speed is the change of position with time,

and acceleration is the change of velocity with time.
The change of energy with time is called power.
Power P is equal to the amount of energy converted from one form to
another (ΔE ) divided by the time (Δt ) during which this conversion takes
place:
Power is measured in units of joules per second, a metric unit known as a
watt (W). One watt of power would raise a 1-kg mass (with a weight
of 10 newtons) a height of 0.1 meter each second.
Some Different Units of Measurement
Power

The English unit for electric power is the watt, but a
different English unit is used for mechanical power.


A horsepower is defined as 550 foot-pounds per second.
This definition was proposed by the Scottish inventor
James Watt because he found that an average
strong horse could produce 550 foot-pounds of work
during an entire working day.

One horsepower is equal to 746 watts.
Human Power



A human can generate 1500 watts
(2 horsepower) for very short periods of time, such
as in weightlifting.
The maximum average human power for an 8-hour
day is more like 75 watts (0.1 horsepower).
Each person in a room generates thermal energy
equivalent to that of a 75-watt light bulb. That’s
one of the reasons why crowded rooms warm up!
Working It Out
Power



A compact car traveling at 27 m/s (60 mph) on a level highway
experiences a frictional force of about 300 N due to the air
resistance and the friction of the tires with the road.
Therefore, the car must obtain enough energy by burning
gasoline to compensate for the work done by the frictional
forces each second:
This means that the power needed is 8100 W, or 8.1 kW.
 This is equivalent to a little less than 11 horsepower.
Paying for it!
Working It Out
Power

How much electric energy does a motor running at 1000 W
for 8 h require?
ΔE
= P Δt
= (1000 W)(8 h)
= 8000 Wh


This is usually written as 8 kilowatt-hours (kWh). Although this
doesn’t look like an energy unit, it is—
(energy/time) × time = energy.
The energy used by the motor in 1 h is
ΔE
= P Δt
= (1000 W)(1 h)
= (1000 J/s)(3600 s)
= 3,600,000 J

In other words, 1 kWh = 3.6 million J.
Conceptual Question
Power

Question: How much energy is required to
leave a 75-watt yard light on for 8 hours?
Answer:
ΔE = PΔt
= (75 watts)(8 hours)
= 600 watt-hours
= 0.6 kWh.