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Energy, Work, and Power
What is Energy?
 Energy, in physics, is defined as the
capacity to do work.
 There are many different forms of energy.
List some types of energy…
 In this chapter, we are going to focus on
gravitational potential and kinetic energy.
If energy is the ability to do work, what is work?
 Mechanical energy transferred by a force
(e.g. gravitational force, friction, applied force) acting on an object
over a measured displacement

I.e., if work is done on an object, the object’s mechanical energy changes
as a result.
 Measured in Newton∙Metres (N∙m) or Joules (J)
 Scalar quantity
•Is work being
done in these
pictures?
• What force is
doing work?
•What on?
Defining Work: When Force is Constant
W = F Δd cosθ
 W = Work (N∙m or J)
 F = Force doing the work (N)
 Δd = displacement (m)
 Θ = angle between F and Δd when placed
tail to tail, always less than 180˚
Positive Work
 When W > 0, the object has gained mechanical
energy due to the force acting on it.
W = F Δd cosθ
 If 0 ≤ θ < 90˚ (i.e., the force has a component
that acts in the same direction as the
displacement)
 Identify situations in which positive work is done.
Zero Work
 When W = 0, zero mechanical energy has been
transferred to the object
W = F Δd cosθ
 If F = 0
 If Δd = 0
 If θ = 90˚ (i.e., F
Δd)
 Describe situations in which zero work is done.
Negative Work
 When W < 0, the object has lost mechanical
energy due to the force acting on it
W = F Δd cosθ
 If 90˚< θ ≤ 180˚ (i.e., the force has a component
that acts in the opposite direction as the
displacement)
 Describe situations in which zero work is done.
Work Examples
 A 0.90 kg book on a level table is pushed with a
force of 15 N over a distance of 6.0 m. A force of
friction of 2.0 N opposes this motion.



How much work does the normal force do on the book?
How much work does the applied force do on the book?
How much work does friction do on the book?
Work Examples
A hockey puck (m = 0.20 kg) slides along a patch of rough
ice (µk = 0.060) and stops after travelling for 25 m.
Draw
a FBD for the puck.
Determine the work done by the friction.
What work is done by the normal force?
Defining Work: When Force Varies
 When force varies over the displacement, the
work done is the area beneath the forcedisplacement graph
 Positive area = positive work done
Negative area = negative work done
Homework on Work
PG. 229 # 1-5, 7-8
Kinetic Energy
 Kinetic Energy (Ek) is the energy of
an object due to its motion.
Ek = ½ mv2
Ek = kinetic energy (J)
m = mass (kg)
v = velocity (m/s)
KE Example
A 95 g donut falls from a table and hits the floor.
The maximum KE of the donut during its fall is 2.6 J.
When does the donut achieve maximum KE?
Calculate the donut’s maximum speed.
KE Conceptual Questions
 As a car leaves a small town, the driver
presses on the accelerator until the speed
doubles. By what factor did the car’s
kinetic energy increase?
 Two cars are travelling
at the same speed. Car A is
twice the mass of car B.
How does car A’s KE
compare to car B’s?
KE Conceptual Questions
 Examine the pictures which follow, and answer the
following questions:





Which object has the greatest velocity?
Work is being done on which of the objects in the photos?
What force is doing the work in each case?
Which objects are probably losing kinetic energy?
Which object has the greatest amount of kinetic energy?
KE Conceptual Questions
Relating Kinetic Energy & Work
W = ΔEk
 Assumptions:
 All
work done gives the system kinetic energy only
 Constant force provides constant acceleration
 Force and displacement are parallel
 The formula for kinetic energy is derived using
work
Homework on Kinetic Energy
PG. 207, 11A-D
PG. 216, 19-21
PG. 226, 23-26
Gravitational Potential Energy
 Gravitational Potential Energy (Eg) is
the energy of an object because of its
position relative to a lower position.
Δ Eg = mg Δh
Δ Eg = change in gravitational potential energy (J)
m = mass (kg)
Δh = change in height (m)
GPE Examples
 Jose Guerra, an 85 kg Olympic diver from Cuba, climbs
to the top of a diving platform at constant velocity. As a
result, he gains 15 kJ of energy, with respect to the
ground. How high is the platform from the ground?
The Importance of Reference Points
Δ Eg = mg Δh
 E.g. A 75 kg skydiver jumps from a plane
1.5 km from the ground. What is her GPE with respect
to:
a) the airplane?
b) the ground?
The amount of GPE an object has is relative.
Relating GPE and Work
W = ΔEg
 Assumptions:



Work done gives system GPE only
Object is lifted at constant velocity
Force and displacement are parallel (θ = 0º)
 The formula for gravitational potential energy
is derived using work.
GPE Conceptual Questions
 Object A has twice the mass of object B.
B is 4.0 m above the ground, and A is 2.0 m
above the ground.
Which has the greater amount of GPE?
 For A and B of the previous question:
Both A and B are lowered 1.0 m.
Which has the greater amount of GPE now?
GPE Conceptual Questions
 You carry a heavy box up a flight of
stairs at constant velocity. Your friend
carries an identical box on an elevator
to reach the same floor as you.
Who did the greatest amount of work
(against gravity)? Explain.
GPE Conceptual Questions
 Examine the pictures which follow, and answer the
following questions:



What object do you think has the greatest amount of GPE?
Which objects clearly illustrate that GPE may be
converted into KE?
What other forms of potential energy can you think of,
besides GPE?
GPE Conceptual Questions
Homework on GPE
p. 235 # 3-6
Law of Conservation of Energy
Energy is neither created nor
destroyed.
It may only be converted from one form to
another or transferred from one object to
another.
Law of Conservation of Mechanical Energy
 The total mechanical energy is the sum of the gravitational
and potential energy.
 Total mechanical energy is conserved (so long as work is
done by conservative forces):
ET = ET’
Eg + Ek = Eg’ + Ek’
ET = total mechanical energy (J)
Eg = gravitational potential energy (J)
Ek = kinetic energy (J)
Conservation Conceptual Questions
 How does the car’s total mechanical energy, kinetic
energy, and gravitational potential energy compare A, B
and C?
A
C
B
Conservation of Mechanical Energy
1
2
mgh  mv  ET
2
Conservation of Mechanical Energy
Conservation Conceptual Question
The masses of the cars in the picture below are
identical. All four cars are released from rest
simultaneously from point A.
Which car is travelling the fastest by point B?
Example Problem
An astronaut on the moon, stands on a cliff and
drops a 20 kg boulder from a height of 30 m. On
the moon, g is 1.6 N/kg.
Use conservation of energy to calculate the speed
of the boulder:
a) Just before it hits the ground.
b) 10 m from the top of the cliff.
Homework on Energy
Conservation
P. 241 # 1-3
Conservative and Non-Conservative Forces
 The box shown can travel any one of
four paths to get to its final
destination, shown.




A then B
C then D
E
F
 In the absence of friction, how does the amount of work done
by gravity compare along each path?
 If friction is present, how does the amount of work is done
by friction compare along each path?
Conservative and Non-Conservative Forces
 The work done by a conservative force does not
depend on the length of the path taken.

E.g. Gravity
 The work done by a non-conservative force
depends on the length of the path taken.


E.g. Friction, air resistance
The longer the path, the more
work done (more energy
removed) from the system by
the force.
Non-Conservative Forces, Work and Energy
 The amount of work done by the non-conservative
force equals the change in the total mechanical
energy of the system:
Wnc=ET’-ET
Wnc = Work done by non-conservative force (N·m)
ET’= Total energy after interaction (J)
ET = Total energy before interaction (J)
Example
 A 65.0 kg skydiver jumps from an airplane at an
altitude of 5.00 × 102 m from the ground. Several
minutes later, she reaches the ground travelling at a
terminal velocity of 8.00 m/s.



What is the skydiver’s total mechanical energy, relative to the
ground, just after she jumps?
What is the skydiver’s total mechanical energy just before
she lands?
How much work did the non-conservative frictional force do?
Mid-Point Assessment

What do the vocabulary terms below mean?
Discuss in your small groups.
Work
Total Mechanical Energy
Potential Energy
Negative Work
Positive Work
Constant Force
Kinetic Energy
Zero Work
Variable Force
Assessment
How are these terms related?
What do you know about these terms?
 Instructions:





WITHOUT TALKING, in your small groups, you will pass around a
piece of paper on which you will construct a mind map.
Your mind maps will show how these terms are related AND what
you’ve learned about the terms.
After 10 minutes, you will be allowed to talk about what you’ve come
up with as a group.
Create a good copy in your groups to post in class.
Don’t forget to copy down your good copy in your notes too!
Mid-Point Assessment
 Example of concept maps:
Mid-Point Assessment
 Some key questions to consider:
 How are work and energy related?
 If zero work is done on an object, does it affect the energy?
What is positive work is done? Negative work?
 How do you calculate work?
POWER & EFFICIENCY
What is Power?
 Rate at which work is done
 Measured in Watts (W)
(1 Watt = 1 Joule/second)
W
P
t
or
P = Power (W)
W = work done (N∙m or J)
E
P
t
ΔE = change in energy (J)
Δ t = time (s)
Power Example
 When doing a chin-up, a physics
student lifts her 40 kg body a
distance of 0.25 m in 2.00 s.
What is the power delivered by
the student's biceps?
What is Efficiency?
 Transforming energy from one form to another
always involves some “loss” of useful energy
 The efficiency of a device describes the amount of
input energy that is converted into the intended
output energy or work.
Efficiency
How much of the input energy goes towards a
“useful” output?
Eo
Efficiency =
x 100%
Ei
Wo
Efficiency =
x 100%
Wi
Eo = useful output energy (J)
Ei = input energy (J)
Wo = useful output work (N∙m)
Wi = input work (N∙m)
Efficiency Example
An electric kettle uses 2000 J of
electrical energy to produce 500 J
of heat energy.
What is the efficiency of the kettle?
Homework
P. 254 # 1-5
Energy, Work & Power Equations
1)
3)
W  Fd cos
E k  21 mv 2
W E
6) P 

t
t
4) E g
2)
W  E
 mgh
5)
ET  Ek  E g
Eout
7) efficiency 
 100%
E in
Work, Energy & Power
TEST YOUR KNOWLEDGE WITH THIS
MINI-TEST!
MINI-TEST
Question 1:
Units for work are joules. This can also be written as:
N/m
B. N∙m
C. N/m2
D. N2∙m
A.
MINI-TEST
Question 2:
Which one of the following statements about work is
correct?
Work is a vector quantity
B. Work has no units
C. Work is a measure of how much energy is created
in a process
D. Work is a scalar quantity
A.
MINI-TEST
Question 3:
Which one of these following statements about power
is correct?
Power is the rate of doing work
B. Power is the rate of change of velocity
C. Power is a vector
D. Power is the potential energy gained when the
mass is raised
A.
MINI-TEST
Question 4:
The power used by a hoist lifting a 50.0 kg mass
through a vertical distance of 4.5 m in 5.0 s is:
A. 10W
B. 45W
C. 100W
D. 450W
MINI-TEST
Question 5:
A theme park roller-coaster carriage starts to run down
a slope. Which of the following statements are true,
ignoring friction and air resistance?
A.
B.
C.
D.
Kinetic energy is transformed to potential energy
Energy is destroyed as heat
Potential energy is transformed into kinetic energy
The total energy at e beginning is bigger than at the
end
MINI-TEST
Question 6:
Which one of the following statements is TRUE:
A. An object at rest has no energy.
B. Gravitational potential energy depends only on
the height of an object.
C. Doubling the speed of a moving object quadruples
its kinetic energy.
D. Things "use up" energy.
Agree or Disagree?
1. “Heat”, “temperature” and “thermal energy” each
describe the same thing.
2. Heat is a substance that resides within an object.
3. A piece of wood and a piece of steel, both removed
from a pot of boiling water and placed in a sealed
container, will cool to different temperatures.
4. Increasing thermal energy will increase
temperature.
Thermal Energy & Heat
 Kinetic molecular theory:

How do the motion of particles in
solids, liquids and gases compare?

Solid
Liquid
Gas
Link 1, Link 2
 Thermal energy:


Measure of the kinetic energy of particles due to their constant
random motion.
Depends on mass, and number of particles in a substance.
 Heat:
 Transfer of thermal energy (through the collision of particles).
Discussion Question
 The picture shows a
kettle of boiling water,
and a mug of boiling
hot tea.
Compare these objects
using kinetic
molecular theory,
thermal energy and
heat.
Temperature
 Measure of the average speed (kinetic energy) of the atoms or
molecules of a substance.
 Measured in units of Celsius (°C),
Fahrenheit (°F) or Kelvin (K).


0°C and 100°C are defined by the
freezing and boiling points of water.
0K is defined as absolute zero,
when the kinetic energy of
particles is zero (no movement).
0K = -273.15°C
TK = TC + 273.15
T = temperature in Kelvin
TC = temperature in Celsius
Kinetic Molecular Theory & Temperature
First Law of Thermodynamics
 The change in energy of a system is the sum of
the work and heat exchanged between a system and
its surroundings:
ΔE = W + Q
ΔE = change in energy (J)
W = Work done on a system (J)
Q = heat (J)
Heat & Temperature
Thermal Equilibrium
 Energy flows from “warmer” objects
to “cooler” objects until they both
achieve thermal equilibrium
(the same temperature).

Transfer of energy occurs
through the collision of particles.
Specific Heat Capacity
 Amount of energy that must be added to raise 1.0 kg
of a substance by 1.0 K.


Larger masses require more heat to achieve a specific rise in
temperature
Different materials have varying capacities to absorb heat.
Table 1: Some Specific Heat Capacities
Substance
Aluminum (solid)
Specific Heat
Capacity (J/kg·°C)
900
Ice (-15°C)
2000
Ethyl alcohol (liquid)
2450
Mercury (liquid)
139
Water (15°C)
4196
Substance
Specific Heat
Capacity (J/kg·°C)
at Constant Pressure
Carbon dioxide gas
833
Nitrogen gas
1040
Water vapour
(100°C)
2020
Specific Heat Capacity
Heat Required for Temperature Change
 To calculate the amount of heat required to raise
the temperature of a quantity of a substance:
Q = mcΔT
Q = heat transferred [J]
m = mass of substance [kg]
c = specific heat capacity of substance
ΔT = temperature change [K or °C]*
*Since K and °C are
1:1, when
temperature changes
are used, both scales
give the same result.
Examples
1.
A 2.5 kg pane of glass, initially at 41°C, loses
4.2 × 104 J of heat. What is the new temperature of the
glass?
2.
A 120 g mug at 21°C is filled with 210 g of coffee at 91°C. All
the heat lost by the coffee is transferred to the mug. The
specific heat capacity of the mug is 7.8 × 102 J/kg·°C.
a.
b.
c.
Write an equation representing the heat gained
by the mug.
Write an equation representing the heat lost
by the coffee.
Calculate the final temperature of the coffee.
Phase Changes
 A beaker of ice is placed on a hot plate.
How do you expect the beaker’s temperature to
change, as more and more heat is added by the
hot plate? Why?
Heat (J)
Heat (J)
Temperature (K)

Temperature (K)
What will happen to the beaker of ice over
time?
Temperature (K)

Heat (J)
Temperature (K)
Its temperature is monitored with a
thermometer.
Heat (J)
 As the ice is heated,
Thermal
energy added
to ice
Temperature (K)
Temperatures
do not increase
during
phase changes
Heat (J)
Increased
av. kinetic energy
of particles
Increase in
temperature
Temperature (K)
Phase Changes
Heat (J)
 When the ice temperature reaches 0°C,
thermal energy goes towards melting the
ice, instead of increasing
temperature.
 Once the ice has melted, the
temperature increases once more.
Phase Changes
 Phase changes require a change in internal energy.
 The amount of energy needed for a phase change is
called the latent heat.
Homework
Pg. 287 #1-10