Download Work and Energy

Unit 7 – Work,
Energy, and
Power
CHAPTER 8 CONCEPTUAL PHYSICS BOOK
Part 2
ENERGY
Energy

Energy (E) – the ability to do work.

Types of energy:
 Mechanical
 Electrical
 Nuclear
 Heat
 Chemical
 Sound
– kinetic + potential
Kinetic Energy

Kinetic energy is the energy of motion.

Many types (like vibrational and rotational)

For now we are talking about translational kinetic
energy – the energy due to motion from one location
to another.
1
𝑚𝑣 2
2

𝐾𝐸 =

Measured in Joules (like work)
Kinetic Energy Example

Which object has greater kinetic energy – a 12 kg
object moving at 20 m/s or a 24 kg object moving at 10
m/s?
1
2
1
2
12 202 = 2400 𝐽

𝐾𝐸1 =

𝐾𝐸2 =

Note that KE is directly proportional to 𝑣 2 , so for
example as v triples, KE goes up by a factor of 9.
24 102 = 1200 𝐽
Work-Energy Theorem

When work is done on an object, the result is a change in the
object’s kinetic energy.
𝑊 = 𝐾𝐸𝑓 − 𝐾𝐸0
or

𝟏
𝟏
𝟐
𝑾 = 𝒎𝒗𝒇 − 𝒎𝒗𝟐𝟎
𝟐
𝟐
This theorem deals with the work done by a net external force
(not an individual force, unless it is the only force).
Work-Energy Theorem Example 1

Calculate the work required to take a 800 kg car from rest to
100 m/s.
𝑚
100
𝑠

𝑚 = 800 𝑘𝑔, 𝑣0 = 0, 𝑣𝑓 =

𝑊 = 𝑚𝑣𝑓2 − 𝑚𝑣02 “from rest” means that the second part goes away.

𝑊=
1
2
1
2
1
2
800 1002 = 4,000,000 𝐽
Work-Energy Theorem Example 2





A 6.4 kg object is pushed by a force of 15 N, resulting in a
displacement of 12 m in the same direction as the push. If the
object’s final speed is 10 m/s, find the initial speed of the
object.
1
𝑚𝑣𝑓2
2
1
𝑊=
− 𝑚𝑣02 use 𝑊 = 𝐹𝑑
2
1
1
15 12 = 6.4 102 − (6.4)𝑣02
2
2
180 = 320 − 3.2𝑣02
𝑣02 = 43.75 → 𝑣0 ≈ 6.6 𝑚/𝑠
Power Example #3

A car accelerates from rest to 20.0 m/s is 5.6 seconds
along a level stretch of road. Ignoring friction, determine
the average power required to accelerate the car if the
mass of the car is 918 kg.
1
1
1
2
2
 𝑊 = 𝑚𝑣 − 𝑚𝑣0 = (918) 20 2
2
2
2
𝑊
184000
 𝑃=
=
= 32,800 𝑊𝑎𝑡𝑡𝑠
𝑡
5.6
≈ 184,000
Gravitational Potential Energy

Potential energy – stored energy.

The higher an object is off of the ground, the
more work gravity can do to it as it falls, and the
faster it will be moving as it hits the ground.

Gravitational potential energy is the energy an
object has by virtue of its position relative to the
surface of the earth.
𝐺𝑃𝐸 = 𝑚𝑔ℎ

Measured in Joules.
Potential Energy Example

Calculate and compare the gravitational potential energies of
the two objects: Object 1 has a mass of 35 kg and is at a height
of 10 m. Object 2 has a mass of 10 kg and is at a height of 35 m.

𝐺𝑃𝐸1 = 35 9.8 10 = 3430 𝐽

𝐺𝑃𝐸2 = 10 9.8 35 = 3430 𝐽

They have the same potential energy.
Conservative vs.
Nonconservative Forces

Conservative force – total Work on a closed path is zero. (ex: gravity)
Gravity- down
Motion- up

-W
+W
Gravity- down
Motion- down
Nonconservative force – total Work on a closed path is NOT zero. (ex: friction)
Friction - right
Motion- left
-W
-W
Energy
12
Friction – left
Motion - right
Conservation of Energy

Law of Conservation of Energy – Energy cannot be
created or destroyed, only converted from one form to
another.

This means the amount of energy when everything
started is still the amount of energy in the universe
today! (Just in different forms!)
𝑬𝒇 = 𝑬𝟎
Conservation of Mechanical Energy

If non-conservative forces are NOT present (or are
ignored) the total Mechanical Energy initially is equal to
the total Mechanical Energy final.
𝑻𝑴𝑬𝒇 = 𝑻𝑴𝑬𝟎
OR
𝑲𝑬𝒇 + 𝑷𝑬𝒇 = 𝑲𝑬𝟎 + 𝑷𝑬𝟎
Conceptual Example 1: Pendulum

Pendulum - Kinetic and Potential Energy

In the absence of air resistance and friction…
 the

pendulum would swing forever
 example
of conservation of mechanical energy
 Potential
→ Kinetic → Potential and so on…
In reality, air resistance and friction cause mechanical
energy loss, so the pendulum will eventually stop.
Conceptual Example 2: Roller Coaster

Roller Coaster - Kinetic and Potential Energy
With Non-Conservative Forces…

If non-conservative forces (such as friction or air
resistance) ARE present:
𝑴𝑬𝒇 = 𝑴𝑬𝟎 + 𝑾𝒏𝒄

Be careful: Work done by friction is always negative!
(Friction always opposes the motion)

So if friction is present, there is mechanical energy loss.
(The energy is converted into heat and sound.)
Conceptual Example 3: Downhill Skiing

Downhill Skiing - Kinetic and Potential Energy

This animation neglects friction and air resistance until
the bottom of the hill.

Friction is provided by the unpacked snow.
 Mechanical
 Negative
energy loss (nonconservative force)
work
Problem Solving Insights


Determine if non-conservative forces are included.
 If
yes: MEf = ME0 + Wnc
 If
no:
(We won’t be solving this type)
MEf = ME0
Eliminate pieces that are zero before solving
 Key
words: starts from rest (KE0 = 0), ends on the ground
(PEf = 0), etc.
Example 1

A 2.00kg rock is released from rest from a height of 20.0 m.
Ignore air resistance & determine the kinetic, potential, &
mechanical energy at each of the following heights: 20.0 m,
12.0m, 0m (Round g to 10 m/s2 for ease)
Example 1 - Answers
Height
20.0 m
KE
PE
ME
0J
Start Here
2*10*20 = 400 J
400 J
12.0 m
400-240 = 160 J
2*10*12 = 240 J
400 J
0m
400-0 = 400 J
2*10*0 = 0 J
400 J
Then
Use
This
22
Example 2
Find the potential energy, kinetic
energy, mechanical energy, velocity,
and height of the skater at the
various locations below.
Energy
max
23
Example 2 - Answers
1. ℎ = 0, so 𝑃𝐸 = 0 𝐽
3. 𝑣 = 0 at the top, so 𝐾𝐸 = 0 𝐽
1
2
𝑀𝐸 = 1920 𝐽
𝑃𝐸 = 1920 − 0 = 1920 𝐽
1920 = 60 9.8 ℎ so ℎ ≈ 3.3 𝑚
𝐾𝐸 = 60 8 2 = 1920 𝐽
𝑀𝐸 = 0 + 1920 = 1920 𝐽
2. ℎ = 1, so 𝑃𝐸 = 60 9.8 1 = 588 𝐽
𝑀𝐸 = 1920 𝐽
𝐾𝐸 = 1920 − 588 = 1332 𝐽
1
𝑚
2
1332 = (60)𝑣 so 𝑣 ≈ 6.7
2
𝑠