# Energy & Work

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```					Energy & Work
Work involves a change in a system.

   changing an object’s position
   heating or cooling a building,
   generating a image on the TV screen,
   moving a speaker cone to make sound

amounts of work, some things require
more energy than others.
Work is…

F

          d

WFdcos( )

   F = force in Newtons
   d = displacement in meters
   The angle  between F & d
   Joule is the unit of WORK
Work is…

   Work- A quantity that measures the effects of
a force acting over a distance.
   Work is a result of motion in the direction of
the force.
   There is no work without motion (d=0).
   Distance-means distance in the direction of
the force. If a force is vertical and motion is
horizontal, No work is done.
Work is…

   MAXIMUM when  = 0º
   MAXIMUM when Force // Displacement
   MINIMUM when  = 90º
   MINIMUM when Force ┴ Displacement
Question #2

If you push vigorously against
a brick wall, how much work
do you do on the wall?
a) A lot
b) None
c) Without numbers, how
can we know?
d) No idea

There is no work done on
the wall as there is no
displacement of the wall.

WFdcos()
WF0cos()
W=0

What are the units of WORK?

   Work is measured in Newton-meters (N•m) or
foot-pounds (ft•lb)
   A Newton-meter is called a “JOULE” (sounds like
‘jewel’)
– Named after James Prescott Joule (1818-1889)
– British physicist who established the
mechanical equivalence of heat and discovered
the first law of thermodynamics.
Find the work done by gravity when
a 2.0 kg rock falls 1.5 m.

   w = F (d) cos()
   What is the formula for Force (F)
   F = m (g) or F = m (9.8 m/s2)
   w = (m · g) (d) cos()
   w = (2.0kg · 9.8m/s2)(1.5m) cos(0°)
   w = 29 J
Negative Work...
    = 0°
   Cos(0°) = 1

    = 180°
   Cos(180°) = -1
Question #3

How much work is done when a man pushes a car
with an 800 N constant force over a distance of 20
m?
a)   0J
b)   40 J
c)   800 J
d)   16000 J
e)   I’m lost…

How much work is done when a man pushes a car
with an 800 N constant force over a distance of 20
m?
w = F (d) cos()

w = (800 N)(20 m) cos(0°)

w = 16 000 J
Question #4

How much work is done by a woman pulling a
loaded dolly 100 ft with a force of 150 lb at an
angle of 45°?
a)   0 ft-lb
b)   7879.8 ft-lb
c)   10606.6 ft-lb
d)   15000 ft-lb
e)   I’m lost…

How much work is done by a woman pulling a
loaded dolly 100 ft with a force of 150 lb at an
angle of 45°?
w = F (d) cos()

w = (150 lb)(100 ft) cos(45°)

w = 10606.6 ft-lb
Power & Work

   Work can be done at different rates.
   Since work involves the transfer of energy, the
faster work is done, the quicker energy needs to
be transferred.
   Power is the measure of how fast work can be
done.
   In other words, power is the rate at which energy
is transferred.
Power is…

Work Force Displacement  cos()
Power       
Time            Time

   W = work in Joules
   t = time in seconds
   WATT is the unit of power
Question #5

A woman exerts 100 N of force pushing a grocery cart
5 meters in 2.5 seconds. How much power did she
exert?
a) 0 watt
b) 40 watt
c) 200 watt
d) 1250 watt
e) I’m lost…

A woman exerts 100 N of force pushing a grocery cart
5 meters in 2.5 seconds. How much power did she
exert?
Work
Power 
Time
100 N 5 meters
Power 
2.5sec
Power  200 watts
Horsepower

 Horsepower   (hp) is a commonly used
unit of power.
 1hp = 746 watts(W)
For example…

•   Let's carry a box of books up a set of stairs.
•   From experience, we know that running the books up the
stairs takes more energy than walking the same distance
(you would be more tired if you ran).
•   But the amount of work done is the same since the books
weighed the same and moved the same distance each trip.
•   However, the work is done much faster if we run, so
energy must be converted faster.
•   Therefore, more power is required.
For example #2…

   Think of a racecar versus an economy car.
   They both can travel the same distance, but the
race car does it much faster since it is capable of
expending much more energy in much less time.
   This is because the more powerful car can convert
energy quicker.
For example #3…

   Think of an 18-wheeler versus an economy car.
   They both can travel the same distance, but the
economy car does it much faster since it is capable
of expending much more energy in much less
time.
   BUT…
   The truck can carry more weight (exert a greater
force) and is more powerful…
Electrical Power

•   Electrical Power is defined the same way.
•   Work must be done to move electrons through the electrical
devices (i.e.,resistance).
•   More resistance means more work must be done to allow the
device to operate.
•   More electrical power means more energy is being
converted.
•   This electrical energy is supplied by the source of the
electrical current, like a battery or generator.
Energy

 The ability to do work.
 An object has energy if it is able to produce
change in itself or its surroundings.
Energy lets us do work

   “Energy is the ability to do Work”
   Energy is important to all living things in order
to maintain life functions.
   Humans use energy to modify their environment
and perform work.
   Energy is measured by the amount of work it is
able to do.
   The units of energy are joules (J).
Energy exists in different forms

1.   Mechanical energy (moving objects and their positions)
2.   Radiant energy (light and solar energy)
3.   Chemical energy (including the food you eat and fuels we
burn)
4.   Thermal or heat energy (molecules moving faster means
more heat)
5.   Electrical energy (electrons moving through a wire)
6.   Nuclear energy (energy locked in the nucleus of an atom)
Energy can be transferred…

   Fossil fuels like coal and oil can be burned to heat
water that boils into steam that turns a turbine to
generate electricity that you use to operate a
stereo.
   Chemical energy  Thermal energy
   Thermal energy  Kinetic energy
   Kinetic energy  Electrical energy
Energy cannot be created or destroyed.

   In the example of riding a bicycle down a steep
hill, you begin with a lot of potential energy at
the top of the hill and gain kinetic energy as you
coast down the hill.
   If you are not making the kinetic energy
(movement down the hill), where does it come
energy at the top is transformed into kinetic
energy as you speed along.
Mechanical Energy

   Kinetic & Potential
   Kinetic is the energy of moving objects.
KE  1 mv2
2
   Potential Energy is stored energy.


   Gravitational PE is energy due to position.
PEmgh

Mechanical Energy - II

   As you speed down a steep hill on a bicycle, you are moving
and therefore have kinetic energy.
   But where did this energy come from? You probably
already know that it came from your position at the top of
the hill.
   At the top of the hill, you had the ability to do work (move
the bicycle) purely because of where you were. You had the
potential to perform the work of moving the bicycle.
   Whenever you work with mechanical energy, you probably
are dealing with both forms together in the same system.
Potential Energy

 Energy  that is a result of an object’s
position or condition.
 All potential energy is Stored Energy.
–   Pull back on a bow string and bend the
bow. The object then possesses potential
energy.
Potential Energy

   A rock on a table top has more potential energy than when
it is on the ground due to its position.
   This is a form of gravitational potential energy.
   Fuel is an example of chemical potential energy, due to its
ability to burn.
Gravitational Potential Energy

   Depends on mass and height.
   GPE = m(g)h
m = mass
g = acceleration due to gravity
h = height
-What are the Units of GPE?
SI units?

   m = kg
   g = m/s2
   h=m
   PE = (kg · m/s2) * m = N*m = J
Question #6

A man lifts a 2 kilogram book from the floor to the top of
a 1.25 meter tall table. What is the change in the
book’s gravitational potential energy?

a)   0 joules
b)   +2.50 joules
c)   -2.50 joules
d)   +24.525 joules
e)   -24.525 joules

A man lifts a 2 kilogram book from the floor to the top of
a 1.25 meter tall table. What is the change in the
book’s gravitational potential energy?
GPE  mgh
   m 
9.81 2  (1.25m)
GPE  (2kg) 
   s 
GPE  24.525 joules
Question #7

A mouse now pushes a book (2 kg) off the table
(1.25m). What is the change in the book’s gravitational
potential energy?

a)   0 joules
b)   +2.50 joules
c)   -2.50 joules
d)   +24.525 joules
e)   -24.525 joules

A man lifts a 2 kilogram book from the floor to the top of
a 1.25 meter tall table. What is the change in the
book’s gravitational potential energy?
GPE  mgh
   m 
9.81 2  (-1.25m)
GPE  (2kg) 
   s 
GPE  24.525 joules
(REMOVING energy from the book)
Kinetic Energy

 Energy   that appears in the form of
motion.
 Depends on the mass and speed of the
object in motion.
Kinetic Energy

   KE = (1/2)mv2
   m = mass v = velocity
   Unit for energy is Joule (J) it is defined as a
Newton Meter.
SI units?

1 2
KE      mv
2
mass  kilograms
2
 meters 
(velocity) 2          
second 
 meter 
KE  kilog ram               meter  Newton  meter  Joule
second 2 


Kinetic Energy

 Energy  due to motion.
 A brick falling at the same speed as
a ping pong ball will do more
damage.
 KE is dependent on mass.
 KE also depends on speed (v)
Kinetic Energy

Which would affect the kinetic energy of an object
more, doubling its mass or its velocity?

   doubling the mass would result in a doubling of the KE.
   doubling the velocity would quadruple the KE.
Question #8

What is the KE of a 1140 kg (2513 lb) car
driving at 8.95 m/s (20 mph)?

a)   0 joules
b)   5101.5 joules
c)   10203 joules
d)   4.57x104 joules
e)   I’m lost…

What is the KE of a 1140 kg (2513 lb) car driving at
8.95 m/s (20 mph)?
1 2
KE  mv
2
2
1              m  
KE  1140kg   8.95 
2               s 
KE  4.57x104 J
Question #9

What is the KE of 11 pound rabbit running at
302.6 mph? Note: 1 ton = 907.185 kg and 1
mph = 0.447 m/s.
a)   0 joules
b)   5101.5 joules
c)   10203 joules
d)   4.57x104 joules
e)   I’m lost…

What is the KE of 11 pound rabbit running at
302.6 mph? Note: 1 pound = 0.454 kg and 1
mph = 0.447 m/s.
1 2
KE  mv
2
2
1                m 
KE   4.99kg  135.26 
2                s 
KE  4.57x104 J
Recall, Law of Conservation of Energy

   Energy can not be created nor destroyed.
   Energy can change from one form to another.
   The total energy in the universe is constant.
Conservation of Energy

   In a roller coaster all of the
energy for the entire ride comes
from the conveyor belt that
takes the cars up the first hill.
Examples

   A 400 kg roller coaster car sits at the top of
the first hill of the Magnum XL200. If the hill
is 151 ft (46 m) tall, what is the potential
energy of the cart?
   What is the speed of the cart at the bottom
(what do you need to ignore?)
   How much KE and PE does the car have half
way down the hill?

   Energy at Top = Energy at Bottom
   Ignoring friction – assume 100% energy conversion
   Energy at Top
–   GPE = 400 kg x 9.8 m/s2 x 46 m = 180 320 Joules
–   KE = 0
   Energy at Bottom
–   GPE = 0
–   KE = 1/2 x 400 kg x v2
   180 320 = 200 v2
   Velocity at Bottom = 30 m/s = 67 mph

   Energy at Top = Energy at Bottom
   Energy at Halfway point?
–   1/2 PE = 90 160 J
–   1/2 KE = 90 160 J
   Speed at Halfway point = ?
–   1/2 of 30 m/s = 15 m/s = 33.5 mph
   NO !!!!!!
–   1/2 mv2 = 90 160
–   Velocity = 21.2 m/s = 47.5 mph
The End 

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