Work & Energy
Conceptual Physics
Intro Discussion
• Twinkie Article
• What is energy?
• What provides humans energy?
• Where does our energy go?
• Can energy just disappear/be destroyed?
• What happens if we don’t have an input of energy?
• What is the work that the human body does?
• Energy Input vs. Output
What is Energy??
• The ability to do work
• The ability to move things, change things, lift things, destroy things, crush things, kill
things….. The ability to do stuff…..
• If an object has Energy, then it is able to move or transform things
•What is work?
•
•
•
•
Work occurs when a force acts over some distance
Work is a transfer of energy
When you do work on an object, you transfer energy from you to that object
This means W =∆E or the amount of work done on an object is equal to the gain or loss
of E for that object
• Two categories of work
• 1) When you do work against another force
• Gravity
• Friction
• 2) When you change an objects speed
Doing Work…
• When something is sped up or slowed down
• When something’s height above the ground is increased
• When the amount of energy that something has changes work is
done on it or by it
• Work is a transfer of energy
• When a force acts over some distance in the direction of
motion…
•W = Fd
• W – Work (J)
• F – Force (N)
• d - distance (m)
Examples
Work Examples
• A crate is pushed with a horizontal force of 50 N across the
floor for a distance of 8 m, how much work was done?
• W = Fd
• W= 50 N x 8 m = 400 J
• How much work does it take to lift a 30 kg suitcase onto the table, 1
meter high?
Still use….
W =Fd
oThe Force “F” required to lift an object is equal to its weight
-remember….Weight = mass x gravity
oThe distance, “d” is equal to the height
o Note- it is height in this case not distance because it is only the work you are
doing against gravity and since gravity acts vertically, only the vertical distance
(height) matters
• So W = Fd
• W = (30 kg x 10 m/s2) x 1m= 300 J
Force must be what is
moving the object in order
for it to be doing work
-The direction of the force
must be the same as the
direction of motion
Units for Work/Energy
• Unit of work (energy) is the N·m, or Joule
(J)
•What else can energy be measured in?
• One Joule of energy is equal to 0.239 calories, or 0.000239 Calories
(food)
• What does it mean to say a piece of food has 1oo calories??
8
Power (P)
• The rate at which work is done
• Units  Watts (W)  1 W = 1 J/s
•P = W/ t
• OR since W = Fd we can say
• P = (Fd)/t which since v = (d/t) we can say
• P= Fv is an alternative form of the power equation, and can be used
to express instantaneous power when velocity is not constant
Many types of Energy
• Electrical
• Chemical
• Thermal
• Solar
• Mechanical
• Sound
• Nuclear
Mechanical Energy (ME)
• Gravitational Potential Energy (PE)
• An object is able to do work by virtue of its position above the Earth
• Stored Energy as a result of an objects position
• Is equal to the work done against gravity in lifting it
•PE = Weight x height
• PE = (mg) x h
•PE= mgh
• h  always measured from some reference level, usually ground
• Kinetic Energy (KE)
• An object is able to do work by virtue of its motion
• Energy of Motion
•KE = ½ mv2
• Elastic Potential Energy
• Will be discussed later
Gravitational Potential Energy
• An object is able to do work because of its position
• The amount of PE an object has at a certain height is equal to the work done
in lifting it to that height
• Stored energy b/c of its raised position
• b/c of gravity it has the potential to do work
• Remember W = Fd
• F is equal to ‘mg’ and the ‘d’ is the same as the ‘h’ So W = Fd =
PE = mgh
•Depends on mass, gravity, and the
height to which it is raised
h
Stairs vs. Ramp vs. direct lift
• Raising which of these blocks requires the most work?
• Ans- All the same, since they are all getting moved up to the same
height they require the same amount of work done b/c they all
gained the same amount of PE
• Which requires the least force?
• The ramp, because W = Fd since it has a longer distance to travel, the force is
reduces. The other two since you are lifting it straight upwards require that you
lift with a force equal to the object weight
• In this manner, a ramp can be very useful….. Even though same work….. Reduces
force
Kinetic Energy
• An object is able to do work because of its motion
• The kinetic energy for a mass in motion is
K.E. = ½mv2
• Example: 1 kg at 10 m/s has 50 J of kinetic energy
• Ex. Tank shells
• Ex. Meteor Impacts
• Ball dropped from rest at a height h (P.E. = mgh) hits the
ground with speed v. After ball falls, no PE left, all energy is
now KE. Expect mgh =½mv2
• In this case all of the PE converted into KE. So energy was
conserved.
Work – Energy Theorem
• Work done is equal to the change of Energy of that object
•W=ΔKE
• However much Kinetic Energy an object gains or loses is equal to
the amount of work done by/on it
• Work is a transfer of Energy from one object to another
• Whatever one object loses… the other gains
Conservation of Energy
• Energy can never be created nor
destroyed
• Energy is never lost, only transferred
• This holds true for all forms of
energy
• In any closed system the total
amount of energy remains constant
Transfers of Energy
• Coal Powered Power Plant
• Car driving down the road
• Boulder falling off of a cliff
• Human running
• Hydroelectric powerplant
• A stick of dynamite explodes
• Wind Turbine
• Energy can always change forms but it cannot be lost
Conservation of Mechanical Energy
• All mechanical energy must be conserved in any closed system
• In other words, the sum of all forms of mechanical energy stays
constant
• MEi = MEf
• Or
PEi + KEi = PEf + KEf
PE at the top = KE at bottom
Cons. Of Mech. Energy
(PE + KE) stays constant the whole time
Example problem
• A 500 Kg cart starts from rest and accelerates to a speed of 10 m/s.
• A) What is the carts initial kinetic energy?
• 0 J ….. Starts from rest KE= ½ mv2  v=0
• B) What is the cart’s final kinetic energy?
• KEf = ½ mv2 = ½ (500)(102) = 25,000 J
• C) What is the carts change in energy?
• ΔE = ΔKE = KEf – KEi = 25,000 J – 0= 25000 J
• D) How much work was done on the car?
• Work = ΔE = 25000 J
Example Problem
Elliptical Orbits
• When faster?? When Slower??
• Why??
• Just like falling objects, when you lose ht. you lose PE and gain KE
• So when close to sun we have converted most PE to KE and when
we are far away vice versa
Elastic Potential Energy
•PEE = ½ kx2
• k = spring constant in N/m
• x = amount of compression or stretch in an elastic
object from its equilibrium position
• This is the third type of mechanical energy
• PEE can also be transferred into PEG and KE and Cons.
Of Mech. E also applies to conversions between this
and the other types of ME
Machines
Efficiency of Machines
• Law of C of E says that energy in must equal energy out
• However, often a lot of energy is lost
• Heat, friction, sound, etc.
• Efficiency = (Useful energy out) x 100%
(Energy in)
• Higher the percentage….the more efficient the machine is
Efficiency (cont.)
• Companies seek to find most efficient machines to manufacture, transpor
and develop
• Ex. Gas powered cars are not very efficient, about 10 - 25% efficient
• Electric (hybrid) cars--much more efficient
• Get up to 3 times the mileage of some gas cars
• http://auto.howstuffworks.com/hybrid-car4.htm
• Government standards
100% Efficient?
Problem
• http://www.bbc.co.uk/schools/gcsebitesize/physics/energy/energyef
ficiencyrev3.shtml
Question 1
A power plant burns 75kg of coal every second. Each kg of
coal contains 27 MJ (27 million joules) of chemical energy.
What is the energy output of the power station every sec?
The Solution
 = 75 x 27 million J per sec
 = 2025 million J per sec
= 2025 million J/s or
(2025 megaWatts)
Question 2
• The electrical power output of the power plant is 800MW (800 million
watts). But Question 1 stated that the chemical energy output of the
What has happened to
the rest of the energy?
station was 2025 MW…..So,
The Answer
wasted
• Most of the rest of the energy is
as heat - up the
chimney of the power station, in the cooling towers, and because of
friction in the machinery.
Question 3
• Calculate the efficiency of the power plant as a percentage.
The Solution
• Efficiency = useful power output/total power input
• = 800,000,000 W/2025,000,000 W
• = 0.395 x 100% to create a percentage
• = 39.5%
Simple Machines
A screw applies a small force
over the long distance across
the face of all of its threads at
once to accomplish the same
work as a large force over a
small distance
• wedge, pulley, lever, ramp, screw, wheel and
axle
• Multiply force but applying small force over
greater distance
• Amount of work done is not increased by a
machine
• By law of conservation of energy it is
impossible to multiply energy
Mechanical Advantage
• Usefulness of machines is due to
multiplication of force, not of energy
• Often limited by how much force we can apply, so we apply a
small force over a large distance
• One way to measure how useful a simple
machine is is by measuring its Ideal
Mechanical Advantage
• MA = Force output / force input
You were able to apply a
100 N force on this end
and move the heavy rock
5 cm
By applying
a 10 N
force and
moving this
end 50 cm..
Soo….MA
= 10/1 =
10
Incline Plane
• MA is made up by comparing the
Parallel force by the force of
gravity, on any incline the parallel
force will be much less than the
weight of the object, this is why it
is easier to walk long distance on
low incline than a short distance
and a steep incline or climbing
straight up
Schober Brothers
embark on a hike in
Yosemite Ntnl. Park
Idiots!
Day 1, short
hike…little
wet…. feelin
good.
…..And learn a harsh lesson
about Incline Planes…
This is easy!!
Day 2 Hike -- 2600 ft of vertical climb to top of
Yosemite Falls
2600 vertical feet
Hike on Day 2-- In pain, not even close to
the top
Little higher up the mountain….
Me slumped on a rock
about to vomit….
…………………Will
cant feel his legs
Andy takes picture
and laughs
Get to the top ..Exhausted…. Pass out on a
rock while squirrel eats our granola
The Point…
Activity
Difficulty
Who can do it
Why??
Hike on flat ground
Easy
Anyone with 2 legs
Horizontal motion, do not need
to work against gravity
Hike up mountain via Harder
long switchbacks and
low grade paths
Anyone with 2 legs and
are at least a little bit in
shape
(Day 1 Hike)
Working against gravity to gain PE
but spread out over a long distance.
Longer distance means shorter Force.
Also spread out over long amt. of
time
Hike up mtn. via
Very
steep steps with high Difficult
incline
Andy, 8 year old girls,…
not Will & Jake 
(Day 2 Hike)
Working against gravity to gain
PE over a shorter distance
requires larger force applied in
short time intervals
Direct climb up
mountain face (no
path)
Extremely Only highly trained rock
Difficult
climbers
(would never even
thinking of trying it)
Essentially lifting your entire
weight straight up with every
step. Requires incredible power,
strength and endurance.
The Point…. (cont.)
• The steeper the incline plane… the higher portion of your weight
you are going to have to lift with every step.
• Low incline, medium incline, direct climb all require the same
amount of work because all produce same increase in PE
• Difference is in how that work is performed.
Pulleys
• Like levers, ramps, and screws…. Sacrifices
displacement to achieve a greater force
• By pulling a greater displacement you have to
apply less force
• MA is shown by how many ropes are supporting
the load in this case there are two
• http://en.wikipedia.org/wiki/Pulley
Another Pulley
• MA = 4
• 4 ropes supporting load
• Force applied is 4 times less than 100 N
• So rope must be pulled with 25 N of
force with a distance 4 times greater
than the upward distance the load
moves
Levers
• Pull greater distance on long end but achieve greater force over a
small distance on the short end