Download Chapter 12 Work and Energy

Chapter 12
Work and Energy
TABLE OF CONTENTS
SECTION 1 : WORK, POWER, AND MACHINES
SECTION 2 : SIMPLE MACHINES
SECTION 3 : WHAT IS ENERGY?
SECTION 4 : CONSERVATION OF ENERGY
Objectives
 Define work and power
 Calculate the work done on an object and the rate
at which work is done
 Use the concept of mechanical advantage to explain
how machines make doing work easier
 Calculate the mechanical advantage of various
machines
Section 1 : Work, Power, and Machines
What is Work?
 Work is the transfer of energy to a body by the
application of a force that causes the body to move in
the direction of the force
 Work is done only when a force causes an object
to move in the direction of the force. This is
different from the everyday meaning of work.
 Work Equation
work = force x distance
w=Fxd
Section 1 : Work, Power, and Machines
What is Work?, continued
 Work is measured in joules, J.
Definition of joules
1 J = 1 N x m = 1 kg x
m2
s2
 Because work is calculated as force x distance, it is
measure in unites of Newtons x meters, N x m. These
units are also called joules, J. In terms of SI base
2
m
units, a joule is equivalent to 1 kg x
s2 .
Section 1 : Work, Power, and Machines
Calculating Work : Math Skills
 Imagine a father playing with his daughter by lifting her
repeatedly in the air. How much work does he do with
each lift, assuming he lifts her 2.0 m and exerts an
average force of 190 N?

Step 1 : List the known and unknown values
Force = 190 N
distance = 2.0 m
Work = ? J

Step 2 : Write the equation for work
Work = Force x distance

Step 3 : Insert your information into the equation, and solve.
Work = 190 N x 2.0 m = 380 J
Section 1 : Work, Power, and Machines
Power
 Power is a quantity that measures the rate at which
work is done or energy is transformed.
 Power equation
Power =
𝐖𝐨𝐫𝐤
𝐭𝐢𝐦𝐞
 Power is measured in watts.

A watt (W) is equal to a joule per second (1 J/s)
Section 1 : Work, Power, and Machines
Calculating Power : Math Skills
 It takes 100,000 J of work to lift an elevator 18m. If
this is done in 20s, what is the average power of the
elevator during the process?

Step 1 : List the known and unknown values
Work= 100,000 J

Power = ? W
Step 2 : Write the equation for power
Power =

time = 20 s
𝐖𝐨𝐫𝐤
𝐭𝐢𝐦𝐞
Step 3 : Insert your information into the equation, and solve.
Power =
𝟏𝟎𝟎,𝟎𝟎𝟎 𝐉
𝟐𝟎 𝐬
= 5,000 W
Section 1 : Work, Power, and Machines
Machines and Mechanical Advantage
 Machines multiply and redirect forces
Machines help people by redistributing the work put into them
 They can change either the size or direction of the input force

 Different forces can do the same amount of work

A machine allows the same amount of work to be done by either
• decreasing the distance while increasing the force or by
• decreasing the force while increasing the distance
Section 1 : Work, Power, and Machines
Force and Work Diagram
Section 1 : Work, Power, and Machines
Machines and Mechanical Advantage, continued
 Mechanical Advantage tells how much a machine
multiplies force or increases distance
 Mechanical Advantage Equation
Mechanical Advantage =
𝐨𝐮𝐭𝐩𝐮𝐭 𝐟𝐨𝐫𝐜𝐞
𝐢𝐧𝐩𝐮𝐭 𝐟𝐨𝐫𝐜𝐞
=
𝐢𝐧𝐩𝐮𝐭 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞
𝐨𝐮𝐭𝐩𝐮𝐭 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞
 Mechanical Advantage (MA) has NO units!

The equation is dividing force by force (N/N) or distance by
distance (m/m) so they cancel- there is no unit for mechanical
advantage
Section 1 : Work, Power, and Machines
Calculating Mechanical Advantage : Math Skills
 Calculate the mechanical advantage of a ramp that is
5.0 m long and 1.5 m high

Step 1 : List the known and unknown values
Input distance= 5.0 m output distance = 1.5 m MA= ?

Step 2 : Write the equation for mechanical advantage
𝐢𝐧𝐩𝐮𝐭 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
MA = 𝐨𝐮𝐭𝐩𝐮𝐭
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆

Step 3 : Insert your information into the equation, and solve.
MA =
𝐢𝐧𝐩𝐮𝐭 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝐨𝐮𝐭𝐩𝐮𝐭 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
=
𝟓.𝟎 𝐦
𝟏.𝟓 𝐦
= 3.3
Section 1 : Work, Power, and Machines
Objectives
 Explain the relationship between energy and work
 Define potential energy and kinetic energy
 Calculate kinetic energy and gravitational potential
energy
 Distinguish between mechanical and
nonmechanical energy
Section 3 : What is Energy?
Energy and Work
 Energy is the ability to do work
When you do work on an object, you transfer energy to that object
 Whenever work is done, energy is transformed or transferred
to another system

 Energy is measured in joules, J.

Because energy is a measure of the ability to do work, energy and
work are expressed in the same units.
Section 3 : What is Energy?
Potential Energy
 The energy that an object has because of the
position, shape, or condition of the object is called
potential energy
 Potential energy is stored energy
Elastic potential energy is the energy stored in any type of
stretched or compressed elastic material, such as a spring or a
rubber band
 Gravitational potential energy is the energy stored in the
gravitational field which exists between any two or more objects

*******
Section 3 : What is Energy?
Potential Energy, continued
 Gravitational potential energy depends on both mass
and height
 Gravitational potential energy equation
GPE = mass x free-fall acceleration x height
GPE = mgh
 The height can be relative
The height used in the above equation is usually measured from the
ground
 However, it can be a relative height between two points, such as
between two branches in a tree

Section 3 : What is Energy?
Calculating GPE : Math Skills
 A 65 kg rock climber ascends a cliff. What is the
climber’s gravitational potential energy at a point 35
m above the base of the cliff?
Step 1 : List the known and unknown values
mass= 65 kg
gravity= 9.8 m/s2 height= 35 m

GPE= ? J

Step 2 : Write the equation for gravitational potential energy
GPE = mgh

Step 3 : Insert your information into the equation, and solve.
GPE = 65 kg x 9.8 m/s2 x 35 m = 22,000 J
Section 3 : What is Energy?
Kinetic Energy
 The energy of a moving object due to the object’s
motion is called kinetic energy
 Kinetic energy depends on mass and speed
 Kinetic Energy equation
Kinetic Energy =𝟏
KE =
𝟐
𝐱 𝐦𝐚𝐬𝐬 𝐱 𝐬𝐩𝐞𝐞𝐝𝟐
𝟏
𝐦𝐯 𝟐
𝟐
 Kinetic energy depends more on speed than mass
Section 3 : What is Energy?
Kinetic Energy Graph
Section 3 : What is Energy?
Calculating Kinetic Energy : Math Skills
 What is the kinetic energy of a 44 kg cheetah running
at 31 m/s?

Step 1 : List the known and unknown values
mass = 44 kg

speed = 31 m/s
Kinetic energy = ? W
Step 2 : Write the equation for kinetic energy
𝟏
𝟐
KE = 𝐦𝐯 𝟐

Step 3 : Insert your information into the equation, and solve.
KE =
𝟏
𝟐
× 𝟒𝟒 𝐤𝐠 × (𝟑𝟏 𝐦/𝐬)𝟐 = 𝟐𝟏, 𝟎𝟎𝟎 𝐉
Section 3 : What is Energy?
Other Forms of Energy
 The amount of work an object can do because of the
object’s kinetic and potential energies is called
mechanical energy

Mechanical energy is the sum of the potential energy and the
kinetic energy in a system
 In addition to mechanical energy, most systems
contain nonmechanical energy

Nonmechanical energy does not usually affect systems on a large
scale
Section 3 : What is Energy?
Other Forms of Energy, continued
 Atoms and molecules have kinetic energy

The kinetic energy of particles is related to heat and temperature
 Chemical reactions involve potential energy

The amount of chemical energy associated with a substance
depends in part on the relative positions of the atoms it contains
 Living things get energy from the sun

Plants use photosynthesis to turn the energy in sunlight into
chemical energy
Section 3 : What is Energy?
Other Forms of Energy, continued
 The sun gets energy from nuclear reactions

The sun is fueled by nuclear fusion reactions in its core
 Electricity is a form of energy

Electrical energy is derived from the flow of charged particles, as
in a bolt of lightning or in a wire
 Light can carry energy across empty space

Light energy travels from the sun to Earth across empty space in
the form of electromagnetic waves
Section 3 : What is Energy?
Objectives
 Identify and describe transformations of energy
 Explain the law of conservation of energy
 Discuss where energy goes when it seems to
disappear
 Analyze the efficiency of machines
Section 4 : Conservation of Energy
Energy Transformations
 Energy readily changes from one form to
another
 Potential energy can become kinetic energy

As a car goes down a hill on a roller coaster, potential energy
changes to kinetic energy
 Kinetic energy can become potential energy

The kinetic energy a car has at the bottom of a hill can do work to
carry the car up another hill
Section 4 : Conservation of Energy
Energy Graphs
Section 4 : Conservation of Energy
Energy Transformations, continued
 Energy transformations explain the flight of a ball
 Mechanical energy can change to other forms of
energy

Mechanical energy can change to nonmechanical energy as a
result of friction, air resistance, or other means.
Section 4 : Conservation of Energy
Kinetic and Potential Energy Graph
Section 4 : Conservation of Energy
The Law of Conservation of Energy
 The law of conservation of energy states that
energy cannot be created or destroyed
 Energy doesn’t appear out of nowhere

Whenever the total energy in a system increases, it must be due to
energy that enters the system from an external source
 Energy doesn’t disappear, but it can be
changed to another form
Section 4 : Conservation of Energy
The law of conservation of energy, continued
 Scientists study energy systems

Boundaries define a system
 Systems can be open or closed
When the flow of energy into and out of a system is small enough
that it can be ignored, the system is called a closed system
 Most systems are open systems, which exchange energy with the
space that surrounds them

Section 4 : Conservation of Energy
Efficiency of Machines
 Not all of the work done by a machine is useful work

A machine cannot do more work that the work required to operate
the machine

Because of friction, the work output of a machine is ALWAYS
somewhat less that the work input
 Efficiency is the ratio of useful work out to work in.

Efficiency is usually expressed as a percentage (%)

The efficiency of a machine is a measure of how much useful
work it can do
Section 4 : Conservation of Energy
Efficiency of Machines, continued
 Efficiency Equation
efficiency =
𝐮𝐬𝐞𝐟𝐮𝐥 𝐰𝐨𝐫𝐤 𝐨𝐮𝐭𝐩𝐮𝐭
𝐰𝐨𝐫𝐤 𝐢𝐧𝐩𝐮𝐭
 Perpetual motion machines are impossible

Energy is always lost to friction or air resistance
 Machines need energy input

Because energy always leaks out of a system, every machine needs
at least a small amount of energy input to keep going
Section 4 : Conservation of Energy
Calculating Efficiency : Math Skills
 A sailor uses a rope and an old, squeaky pulley to raise a
sail that weight 140 N. He finds that he must do 180 J of
work on the rope in order to raise the sail by 1 m (by
doing 140 J or work on the sail). What is the efficiency of
the pulley? Express your answer as a percentage.
Step 1 : List the known and unknown values
Work input= 180 J
useful work output = 140 J


Step 2 : Write the equation for kinetic energy
efficiency =

efficiency = ?
𝐮𝐬𝐞𝐟𝐮𝐥 𝐰𝐨𝐫𝐤 𝒐𝒖𝒕𝒑𝒖𝒕
𝐰𝐨𝐫𝐤 𝒊𝒏𝒑𝒖𝒕
Step 3 : Insert your information into the equation, and solve.
efficiency =
𝟏𝟒𝟎 𝐉
𝟏𝟖𝟎 𝐉
= 𝟎. 𝟕𝟖 𝐱 𝟏𝟎𝟎 = 𝟕𝟖%
Section 4 : Conservation of Energy
Concept Map