Chapter 4
Work and Energy
•
Section 1: Work and Machines
•
Section 2: Describing Energy
•
Section 3: Conservation of Energy
Section 1: Work and Machines
Work – the transfer of energy that occurs when a force makes
an object move
• no movement, no work
• direction of the net force indicates where or on what work is
being done
• calculating work:
equation for work: work = force x distance, or:
𝑾 = 𝑭𝒅 Where:
Units for Work:
W = Work
F = force (N)
d = distance (m)
W =Fd
W = (N)(m) = Nm
1Nm = 1 Joule (J)
The unit for work is Joules (J)
Example: How much work is done if Reggie lifts a box, m = 50kg, 1.75 meters?
Solution:
m = 50.0kg
d = 1.75m
Because Reggie is lifting the box
he must exert a force greater
than the weight of the box
𝑊 = 𝑚𝑔
𝑚
𝑊 = 50.0 𝑘𝑔 9.8 2
𝑠
𝑘𝑔𝑚
𝑊 = 490 2 = 490.0 𝑁
𝑠
Solve for work:
𝑊 = 𝐹𝑑
𝑊 = 490.0 𝑁 1.75𝑚
𝑊 = 857.5 𝑁𝑚
𝑾 = 𝟖𝟓𝟕. 𝟓 𝑱
Section 1: Work and Machines
Machine – a device that makes doing work easier
• Machines make doing work easier in three ways:
1. Increasing the force applied to the object
example: a car jack to lift a car to change a flat tire
2. Increasing the distance over which the force is applied
example: using a ramp to raise objects to a height
3. Changing the direction of the applied force
example: a wedge – the vertical force is changed to a
horizontal force
• Work done by machines
 Two forces are involved when a machine is used to do
work:
1. Effort force – the force applied to the machine
2. Resistance force – the force applied by the machine
to overcome resistance
• Conservation of Energy
 You transfer energy to a machine, the machine transfers
that energy to the object
 Energy is neither created nor destroyed, so the work
done by the machine is never greater than the work
done to the machine
 Because of energy losses due to friction, the work done
by the machine is always less than the work done to the
machine
Section 1: Work and Machines
• Mechanical Advantage – the number of times a machine
multiplies the effort force
 Equation for Mechanical Advantage :
𝑴𝑨 =
𝒇𝒐
𝒇𝒊
Where:
MA = mechanical advantage
fo = force out (force applied by the machine)
fi = force in (force applied to the machine)
Example: A claw hammer is used to pull a nail from a board.
If the claw exerts a resistance force of 2500-N to the applied
force of 125-N, what is the mechanical advantage of the
hammer?
Solution: fo = 2,500.0N
𝑓𝑜
𝑀𝐴 =
fi = 125.0N
𝑓𝑖
MA =?
2,500𝑁
𝑀𝐴 =
125𝑁
𝑴𝑨 = 𝟐𝟎
Notice that the force units (N) cancel; mechanical advantage
has no units, it is just a number.
Section 1: Work and Machines
Simple machine – a machine that does work with only one
movement
• There are six (6) simple machines divided into two types:
The lever type
The inclined plane type
Includes:
 Lever
 Pulley
 Wheel and axle
Includes:
 Ramp
 Wedge
 Screw
Compound machine – a machine that consists of two or more
simple machines used together
Section 1: Work and Machines
Lever – a bar that is free to pivot, or turn, about a fixed point.
• There are three classes of levers:
1st class lever – the fulcrum
is between the effort and
the resistance
 Multiplies effort force
and changes its direction
 Examples: crow bars, teeter-totters
2nd class lever – the resistance
force is between the effort
force and the fulcrum
 Multiplies force without
changing direction
 Examples: wheel barrows, doors
3rd class lever – the effort
force is between the fulcrum
and the resistance force
 The effort force is always
greater than the resistance force. MA < 1
 Examples: the fore-arm, fishing poles
If the 3rd class lever has no mechanical advantage, why use
one?
Section 1: Work and Machines
Calculating the mechanical advantage of levers
•
Equation: 𝑴𝑨 =
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒆𝒇𝒇𝒐𝒓𝒕 𝒂𝒓𝒎
,
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒂𝒓𝒎
or: 𝑴𝑨 =
𝒅𝒆
𝒅𝒓
 the distances are measured from the fulcrum to the point
where the forces are acting
Example: If the distance of the effort force is 3-m, and the
distance of the resistance arm is 1-m, what is the mechanical
advantage of the lever?
Solution:
𝑑𝑒
de = 3.0m
𝑀𝐴 =
dr = 1.0m
𝑑𝑟
3.0𝑚
MA = ?
𝑀𝐴 =
1.0𝑚
𝑴𝑨 = 𝟑. 𝟎
Notice the distance units cancel. Remember, mechanical
advantage is just a number.
Section 1: Work and Machines
Pulleys
• The two sides of the pulley are the effort arm and the
resistance arm.
• A fixed pulley changes the direction of the force only, it does
not increase force
• A moveable pulley will increase the effort
• Block-and-tackle – a system of pulleys consisting of fixed
and moveable pulleys. The block-and-tackle will multiply the
effort force
Wheel-and-axle – a machine consisting of two wheels of
different sizes that rotate together
Inclined plane (ramp) – a sloping surface that reduces the
amount of force required to do work
• The same amount of work is done by lifting a box straight up
or by sliding it up a ramp. However, the ramp reduces the
amount of force required by increasing the distance
 Mechanical advantage of a ramp:
𝑴𝑨 =
𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇𝒊𝒏𝒄𝒍𝒊𝒏𝒆
,
𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒓𝒂𝒎𝒑
𝒍
or: 𝑴𝑨 = 𝒉
Example: Jessica uses a ramp 5-m long to raise a box to a
height of 1-m. What is the mechanical advantage of the ramp?
Solution
𝑙
Length =5.0m
𝑀𝐴 =
Height = 1.0m
ℎ
5.0𝑚
MA = ?
𝑀𝐴 =
1.0𝑚
𝑴𝑨 = 𝟓. 𝟎
Section 1: Work and Machines
Screw – an inclined plane wrapped around a cylinder
Wedge – an inclined plane with one or two sloping sides
Mechanical Efficiency (ME)
• Recall that the amount of work done by the machine (work
output) is always less than the work done on the machine
(work input)
• Mechanical Efficiency is the measure of how much of the
work put into a machine is changed into useful output work
by the machine
 Because of friction no machine is 100% efficient. ME will
always be less than 100%
 Equation: 𝑴𝑬 =
𝒘𝒐𝒓𝒌 𝒐𝒖𝒕𝒑𝒖𝒕
𝐱𝟏𝟎𝟎%,
𝒘𝒐𝒓𝒌 𝒊𝒏𝒑𝒖𝒕
or: 𝑴𝑬 =
𝒘𝒐
𝒙𝟏𝟎𝟎%
𝒘𝒊
Example: John is changing a flat tire on his truck. He does
2,500J of work on the jack, while the jack does 2,100J of work
on the car. How efficient is the jack?
Solution
𝑤𝑜
wi = 2,500J
𝑀𝐸 =
𝑥100%
𝑤
wo = 2,100J
𝑖
2,100𝐽
ME = ?
𝑀𝐸 =
𝑥100%
2,500𝐽
𝑀𝐸 = 0.84𝑥100%
𝑴𝑬 = 𝟖𝟒%
Section 2: Describing Energy
Energy – the ability to cause change
• Energy comes in different forms  chemical, electrical,
thermal, etc.
 We will be looking at three (3) types of energy: kinetic,
potential, and mechanical.
• Kinetic Energy (KE)
 KE is energy in a moving object
 Anything that moves has kinetic energy
 Kinetic energy depends of two things:
1. the mass of the moving object
2. the velocity of at which the object is moving
 Equation for kinetic energy:
𝟏
Where:
𝑲𝑬 = 𝒎𝒗𝟐
KE = kinetic energy
𝟐
M = mass (kg)
V = velocity (m/s)
 Unit for energy:
𝑚
𝐾𝐸 = 𝑘𝑔( )2
𝑠
2
𝑚
𝐾𝐸 = 𝑘𝑔 2
𝑠
kgm2
𝐊𝐄 =
= Nm = 𝐉
s2
Section 2: Describing Energy
Example: A ball, m = 1.5-kg, is rolling across the floor towards the
door at 2 m/s. What is the KE of the rolling ball?
Solution
m = 1.5-kg
v = 2.0-m/s
KE = ?
1
𝐾𝐸 = 𝑚𝑣 2
2
1
𝑚 2
𝐾𝐸 = ( )(1.5𝑘𝑔)(2.0 )
2
𝑠
1
𝑚2
𝐾𝐸 =
1.5𝑘𝑔 4.0 2
2
𝑠
𝒌𝒈𝒎𝟐
𝑲𝑬 = 𝟑. 𝟎
= 𝟑. 𝟎 𝑱
𝒔𝟐
Important: Always square the velocity before you do any
multiplication
• Potential Energy
 Potential energy – energy stored due to an object’s
position
 Three types of potential energy:
 Elastic – PE stored by things that stretch or compress
Ex.: rubber bands, springs, pole vault poles
 Chemical – PE stored in chemicals bonds
Ex.: nuclear weapons and fuels
 Gravitational – PE stored by things that are elevated
Ex.: fruit on trees, bouncing balls
Section 2: Describing Energy
• The amount of potential energy can be determined
mathematically. We will focus on gravitational PE
 Equation for gravitational PE:
PE = Potential Energy (J)
𝑷𝑬 = 𝒎𝒈𝒉
M = mass (kg)
g = 9.8 m/s2
H = height (m)
Example: An apple, mass = 0.5-kg, is hanging from a branch
4.0-m above the ground. What is its gravitational PE?
Solution
m = 0.5 kg
𝑃𝐸 = 𝑚𝑔ℎ
𝑚
h = 4.0 m
𝑃𝐸 = 0.5𝑘𝑔 9.8 2 4.0𝑚
𝑠
PE = ?
2
𝑘𝑔𝑚
𝑃𝐸 = 19.6 2
𝑠
𝑷𝑬 = 𝟏𝟗, 𝟔 𝑱
Section 3: Conservation of Energy
• Mechanical Energy – the total amount of potential and
kinetic energy in a system
 Equation: mechanical energy = potential energy + kinetic
energy, or: M E = P E + K E
Example: An object held in the air has a gravitational PE of
480.0J. What is its kinetic energy if it has fallen two-thirds of
the way to the ground?
Solution
a)Before the object started falling ME = PE, so ME
= 480.0J.
b)As the object is falling PE is being converted to
KE.
c)At anytime during the fall ME = PE + KE.
d)When the object is two-thirds of the way down
ME = 1/3PE + 2/3KE.
e)So: KE = 2/3(480.0 J), or KE = 320.0J
• Law of Conservation of Energy: Energy is neither created nor
destroyed
 On a large scale: total energy in the universe is constant
 Consequence: energy can change form:
potential  kinetic
kinetic  thermal
chemical  mechanical
Section 3: Conservation of Energy
• Power – the amount of work done in a certain amount of
time
 Power is a rate
 Equation for calculating power:
 Units for Power: the Watt (W)
pow er =
w o rk
,or : P =
tim e
1W = 1
J
= 1
W
t
kg m 2
s3
s
1 watt is about equal to the power required to lift a glass
of water from a table to your mouth
Example 1: It took 20 seconds to move a refrigerator, You did
3,150 J of work in the process. How much power was required
to move the refrigerator?
Solution P = W
t
P =
3 ,1 5 0 J
20s
P = 1 5 7 .5
J
= 1 5 7 .5 W
s
Example 2: It took you 1.5 s to lift a 10-kg box of the floor to a
height of 1.0-m. How much work did you do on the box, and
how much power was required to do this?
Solution
t = 1 .5 s
m = 1 0 .0 k g
F = W (e ig h t) = m g
F = 1 0 k g (9 .8
d = 1 .0 m
W = ?
P = ?
F = 98
kg m
s2
m
s2
)
W = Fxd
W = 9 8 N (1 .0 m )
W = 98N m = 98J
= 98N
P =
W
t
P =
98J
1 .5 s
P = 6 5 .3 3
J
s
= 6 5 .3 3 W