2.3 Work, Energy and Power
2.3.1 Outline what is meant by work.
Work…
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 First a demo: Everybody stand up
 Hold a couple of books and walk across the room.
 How much work was done to the book?
 Any? A lot? A little? None?
Is the product of the magnitude of the displacement and the component of the force acting in the direction
of the displacement
Is the force applied over a distance
When a force acts upon an object to cause a displacement of the object
two key ingredients:
 ______________
 ______________
Everyday examples:
1. a horse pulling a plow through the field
2. a father pushing a grocery cart down the aisle of a grocery store
3. a weightlifter lifting a barbell above his head
4. Olympian launching the shot-put
 Can you identify the two parts in each example?
Are these examples of work?
1. A teacher applies a force to a wall and becomes exhausted. Y or N
2. A book falls off a table and free falls to the ground. Y or N
3. A waiter carries a tray full of meals above his head by one arm straight across the room at constant
speed. Y or N
4. A rocket accelerates through space. Y or N
Or… W = F s cosΘ
 s is displacement or Δs
 F is force applied
 Θ is the angle between the force and the displacement vector
Notice that the ___________________ of a force alone does not constitute work.
Work can only be done when looking at the force applied ___________________to the displacement.
 Most of the time F is in the direction of d so θ = 0° and cos 0° = 1 so… it all works out.
Consider theta: (draw the chart)
Three basic situations
 Pay attention to the direction of the displacement and the applied force.
 Ex. A car being pushed up a ramp
 Consider “the sign”:
 If force and displacement are in the…
 Same directions, + W
 ______________ directions, - W
 Perpendicular directions, W = 0
 From all that we can say that the total work done is dependent on the total force applied. So….
 Wnet = Fnet d cosΘ
 So, what are the units?
 If we break it down W = F * d => ? = N * m => J = N * m
 Basic question:
 What work is done to lift your Physics book (m=12kg) up 1 m?
 What work is done to carry the book 1 m across the room?
2.3.3 Solve problems involving the work done by a force.
 Try this:
What is the work done on a vacuum cleaner pulled 3m by a force of 50N at an angle of 30° above the
horizontal?
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The angle of the force means we have to find the force acting in the direction that the bag moves. It
moves in the x-position, so we will use the Fx component. The upward component doesn’t do any
work as the y-position doesn’t change.
A few more Practice Problems:
1) A 20kg suitcase is raised vertically 3m above a platform by a conveyor belt. How much work is done on
the suitcase?
2) A 100 N force is applied to move a 15kg object a horizontal distance of 5m at constant speed.
3) A 100N force is applied at an angle of 30° to the horizontal to move a 15kg object at a constant speed
for a horizontal distance of 5m.
4) An upward force is applied to lift a 15kg object to a height of 5m at constant speed.
Work Space
2.3.2 Determine the work done by a non‑ constant
force by interpreting a force–displacement graph.
 This work equation is only applicable if the force is
constant.
 In real life there are lots of non-constant forces.
 We can use a graph to determine work done.
 On a Force/Displacement graph the area under the graph
is the work done.
2.3.7 List different forms of energy and describe examples of the transformation of energy from one form
to another.
Energy – Flow Chart
2.3.4 Outline what is meant by kinetic energy.
Kinetic Energy
 Associated with objects in __________
 Depends on both an object’s __________ and __________
 It is a __________ quantity
 Formula
 Kinetic energy = 1/2 *mass*speed2
 KE= ____________
 The unit of KE is joule(J)
 Notice: If the speed is doubled the energy is ____________
Example: A bowling ball and a volleyball roll at the same speed.
 Which has more kinetic energy? ____________
2.3.11 Solve problems involving momentum, work, energy and power.
Example: A 7kg bowling ball moves at 3 m/s. How fast must a 2.45 g ping pong ball move to have the same
kinetic energy as the bowling ball?
 KE=1/2 mv2
 Practice:
1) Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.
2) If the roller coaster car in the above problem were moving with twice the speed, then what would be its
new kinetic energy?
3) Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of
12000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?
4) A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate
its new kinetic energy if it is moving at 30 mi/hr. (HINT: use the kinetic energy equation as a "guide to
thinking.")
2.3.5 Outline what is meant by change in gravitational potential energy.
Potential Energy
 Associated with an object that has the potential to move because of its _____________
 Depends on the interaction with its _____________
 store energy as the result of its position
 Gravitational potential energy - Potential energy due to _____________
 the energy stored in an object as the result of its vertical position or height.
 PEg = mass*free-fall acceleration*height
 PEg = _____________
 Notice that PEg is dependant on free-fall acceleration being _____________. Meaning this usually only
applies to things _____________.
 Also notice that g and h _____________ properties of the actual object.
 The higher that an object is elevated, the _____________ the gravitational potential energy
 a doubling of the height will result in a _____________ of the gravitational potential energy
Is it possible to have a negative potential energy? _____________
 Can an object have both a positive potential energy and a negative potential energy?
 How is h defined? - Relative to a “zero”
 What can be a “zero”? - Anything can be defined as “zero”
 Discussion: A ball that falls from one building rooftop to another buildings rooftop. Where is zero?
(Draw the picture)
Springs!!! – Elastic Potential Energy
 a device which can store elastic potential energy due to either _____________ or _____________
 _____________ is required to compress a spring
 the amount of force is _____________ _____________ to the amount of stretch or compression
 _____________ _____________ – when a spring isn’t being stretched or compressed
 Fspring = k * x
 ______ is the spring constant
 Small for flexible springs
 Large for stiff springs
 Units of (N/m)
 ______ is the amount stretched or compressed
 ___________ length
 Length of spring when no external forces are acting on it.
 Nothing is pulling or pushing it.
2.3.11 Solve problems involving momentum, work, energy and power.
PEtotal = PEg + PEspring
 PEelastic = ½*spring constant*(distance compressed or stretched)2
 PEelastic = ½kx2
Practice Problems
 A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top.
If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential
energy of the loaded cart at the height of the seat-top?
 If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance
of 0.90 meters, then how much work is done on the loaded cart?
 A 70kg stuntman is attached to a bungee cord with an un-stretched length of 15m. He jumps off a bridge
spanning a river from a height of 50m. When he finally stops, the cord has a stretched length of 44m. Treat
the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of
the bungee cord is 71.8N/m, what is the total potential energy relative to the water when the man stops
falling?
2.3.6 State the principle of conservation of energy.
Energy
 The ability to do ___________
 Potential energy is the energy of position
 Kinetic energy is the energy of motion (depends on speed and mass)
 ___________ energy= Potential + Kinetic energy
The Law of Conservation of Energy
 States that energy can be neither ____________ nor ____________, it is conserved
 Energy can transform from one form to another, but it always adds up to the ____________ amount.
Ex.Mechanical energy is converted into thermal energy whenever you bounce a ball. Each time the
ball hits the ground, some of the energy of the ball's motion is converted into heating up the ball, causing
it to slow down at each bounce
 Energy Transformation - Energy can neither be created nor destroyed, but it can be changed into different
forms of energy…
 The forms include: thermal (heat), chemical, electrical, sound, light, nuclear
Conservation of Energy
 Mechanical Energy is:
 the energy which is possessed by an object due to its __________ or due to its _________.
 the total kinetic energy and potential energy associated with an object
 ME = KE + PEtotal
 Mechanical energy is just a classification, not another type of energy.
 Nonmechanical energy:
 Other forms of energy
 Ex. light, sound, heat
 Mechanical energy is conserved (in the absence of friction)
 So => initial mechanical energy = final mechanical energy
 So => MEi = MEf
 So => KEi + Ptotal,i = KEf + Petotal,f
Ex.The question is if a 75g egg falls off a 1m counter top what is it’s total ME half way down?
 To better understand lets remember a few things.
 First Vf = Vi + aΔt
 Second Δx = ½ (Vi + Vf)Δt
Time
0s
.1s
.2s
.3s
.4s
.5s
Vf
KE
Δx
Height
PE
ME
Conservation of Energy
 Mechanical energy is not conserved in the presence of Kinetic ___________.
 So what happens to the energy?
 Ex rubbing your hands together
 Total energy is always conserved, but mechanical energy is _____________.
 Mechanical energy is converted in to…
 Now can you answer this basic question: If an object (m=10kg) falls from a height of 10 m, what is it’s:
 Potential and kinetic energy at the top ______________
 Potential and kinetic energy just before hitting the ground. _____________
 Practice:
1. Starting from rest, a child zooms down a frictionless slide from an initial height of 3m. What is her
speed at the bottom of the slide? Assume she has a mass of 25kg
2. A frog is sitting on a rock. It sees a cat that is trying to eat it. The frog jumps directly up with an initial
velocity of .85m/s. What is the total height the frog jumps?
3. The cat then jumps directly upward 1.2m. What was the initial velocity of the cat’s jump?
2.3.9 Define power
POWER!!!
 What is power? Let’s look at:
 a rock climber takes 30min. to elevate his body up a few meters along the side of a cliff.
 a trail hiker, who selects the easier path up the mountain, might elevate his body a few meters in
10min.
 They both do the same amount of work.
 Which one had more power? ______________
 is the rate at which ____________ is done
 or the rate at which ___________ is consumed
 P = ________
 The more power you have the _________ work you can do in the __________ time.
 The more power you have you can do the __________ amount of work in a __________time.
 There is an ____________ relationship between work and time
 This equation shows us that a powerful machine is both strong (big force) and fast (big velocity).
 Ex. A powerful car engine is strong and fast.
 Equations for power are:
 P = W/t
 P = F (d/t)
 P=Fv
 P = ΔE/t
 What units? The SI unit of power is the _______________
 1 watt is = 1________ / second
 W=J/s
 Horsepower is also a unit.
 1 horsepower = __________ watts
 Hp = 746W
 Examples of power
 A dim light bulb 40 W
 A really bright bulb 500 W
 Indoor Christmas light .7 W
 Outdoor Christmas light 7 W
2.3.11 Solve problems involving momentum, work, energy and power.
 Examples situation
 A 193kg curtain needs to be raised 7.5m, in 5s. You have 3 motors with power ratings 1.0kW, 3.5kW
and 5.5kW. Which motor is best for the job? How much time would it take for each motor to do the
same amount of work?
 Examples situation
 Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min.
 1) What is the power delivered by the horses?
 2) How much work is done by the two horses?
 Practice:
 Two physics students, Will N. Andable and Ben Pumpiniron, are in the weightlifting room. Will lifts the
100-pound barbell over his head 10 times in one minute; Ben lifts the 100-pound barbell over his head 10
times in 10 seconds. Which student does the most work? Which student delivers the most power?
 During a physics lab, Jack and Jill ran up a hill. Jack is twice as massive as Jill; yet Jill ascends the same
distance in half the time. Who did the most work? Who delivered the most power? (plug in fake numbers)
 When doing a chin-up, a physics student lifts her 42.0-kg body a distance of 0.25 meters in 2 seconds. What
is the power delivered by the student's biceps?
 Mr. B gets bored after school one day and decides to play in the hall. He sits in his rolling chair and pushes
off the wall with 12N of force producing 30W of power. What was his resulting speed he traveled down the
hallway?