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Work, Energy, and Power
Work
What is Work and Energy?
• Energy(E)- the ability to do work
• Work (W)- A change in energy (ΔE) or the product of Force and
distance (d)
– W=Fd
– Work is only being done when components of the applied force are
parallel to the displacement
• Both are scalar and are measured in joules
– 1 joule=kg m2/s2 or 1 joule=N*m
When is work being done?
• If a hold a 30 kg object at a height of 1.5 meters is work being
done?
• I am exerting energy….
• Work is NOT being done on the OBJECT, work is being done on
muscles, but not the object
• The distance that the object has moved is zero so no work is done
• W=Fd W=F0
Example
• If the same 30 kg object was pushed to the right with an
acceleration of 2m/s2 for 2.0 meters, how much work is done on
the object?
• W=Fd
• Remember F=ma
• M=30 kg
• a=2 m/s2
• d=2.0 m
• W=?
• F=ma
• F=30(2) = 60N
• W=Fd
• W=60(2) =120 J
Example
• If I were to lift the 30.0 kg object up off the ground to a height of
1.5 m, how much work is done on the object?
• When an object is being lifted against gravity, use g for the
acceleration (9.8 m/s2)
• W=mgd
• m=30 kg
• g=9.8 m/s2
• d=1.5 m
• W=?
• W=30(9.8)(1.5) W= 440 J
Clicker Question
• A 3.0 kg pineapple is held 1.2 m above the floor for 15 s. How much
work is done on the pineapple?
• A)0.25 J
• B)54 J
• C)35 J
• D) 0 J
Clicker Question
• A 10.0 kg pumpkin is moved horizontally 5.00 m at a constant
velocity across a level floor using a horizontal force of 3.00 N. How
much work is done in moving the pumpkin?
• A) 30 J
• B) 294 J
• C) 15 J
• D) 0 J
Example- Honors
• A 50.0 kg banana box is pulled 11.0 m along a level surface by a
rope. If the rope makes an angle with the floor of 35o and the
tension in the rope is 90.0 N, how much work is done on the box?
• Use the force component that is parallel to the displacement!
• m=50.0 kg
• d=11.0 m
• Theta=35 degrees
• Fapplied=90.0 N
• W=?
• W=Fd
• F(x)=?
Example
• A 1385 kg car traveling at 61 km/h is brought to a stop while
skidding 42 m. What is the work done on the car by frictional
forces?
• m=1385 kg
• vi-=61 km/hr
• Vi=17 m/s
• Δx=42 m
• Vf=0
• W=?
• W=Fd
• F=?
• F=ma
Nonconservative Forces
• The work produced by nonconservative forces are dependent on
the paths taken
• Friction and air resistance are types of nonconservative forces
• A conservative force, such as gravity, are not dependent on the
path taken
How does an angle impact work?
If you have a 10.0 kg
object, how much work is
done on the object if it is
lifted 1 meter straight off
the ground? On a ramp
that is 30 degrees off the
ground (A)? 60
degrees(B)?
A
1.0m
B
How does an angle impact work?
Wf = Ffd
Ff = ukFN
FN gets larger
as the angle gets
smaller
So… Ff gets smaller,
But you still need to
Add the Fg
So the work
Increases with a
Higher angle
A
1.0m
B
Continued
• Work against gravity will not change, however!
• If they end at the same height the work against gravity will not
change
• The amount of force needed will change according to the angle,
but the distance will change as well to get to the same height
• So the work against gravity is the SAME
Work, Energy, and Power
Potential Energy
Potential Energy
• Energy can either be potential energy or kinetic energy
• Potential energy is stored energy
• Examples
–
–
–
–
Chemical
Elastic (bungee cord, trampoline, bow)
Electrical (static charges)
Gravitational potential energy
Energy can be converted into different forms by doing work
Gravitational Potential Energy
• Due to an object’s position (height) measured relative to a
reference point
• Gravitational Potential Energy – Ep (or GPE)
• Ep=mgh
• m=mass
• g=9.8 m/s2
• h=height
Example
• A 15.0 kg textbook is sitting on a 1.20 m tall table. If the book is
lifted 0.80 m above the table, how much gravitational potential
energy does it have:
• With respect of the table?
• With respect to the ground?
Clicker Question
• A 1400 kg roller coaster is moved to the top of a track that is 100 m
above the lowest part of the track. What is the gravitional
potential energy of the coaster?
• A) 2000 J
• B) 1.4 x 104
• C) 34000 J
• D)1.4 x 106 J
Spring/Elastic Potential Energy
• The energy available for use in deformed elastic objects
– Rubber bands, springs in trampolines, pole-vault poles, muscles
• For springs, the distance compressed or stretched = x
• Spring constant (k) depends on stiffness of spring, measured in
N/m
– Force needed to stretch the spring 1 meter
Example
• When a 2.00 kg mass is attached to a vertical spring, the spring is
stretched 10.0 cm such that the mass is 50.0 cm above the table
• What is the gravitational potential energy associated with the mass
relative to the table?
• What is the spring’s elastic potential energy is the spring constant
is 400.0 N/m?
Work, Energy and Power
Kinetic Energy
Kinetic Energy
• Energy of motion
• scalar
• Ek=1/2 m v2
– Ek= kinetic energy
– m=mass
– v=speed
Example
• A 60.0 kg student is running at a uniform speed of 5.70
m/s. What is the kinetic energy of the student?
• Ek=1/2 m v2
• m=60 kg
• v=5.70 m/s
• Ek=?
• Ek=1/2(60)(5.7)2
• Ek=975 J
Clicker Question
• The kinetic energy of a 2.1 kg rotten tomato is 1000 J. How fast is it
moving?
• A) 15.4 m/s
• B) 31 m/s
• C) 961 m/s
• D) 4000 m/s
Work Energy Theorem
• If a net force is acting on an objet then the object must be
accelerating
• The change in kinetic energy is proportional to the net force
• ΔEk=Fnetd
• d=distance
Example
• A sprinter exerts a net force of 260 N over a distance of 35 meters.
What is his change in kinetic energy?
• ΔEk=Fnetd
• Fnet=260 N
• d= 35 m
• ΔEk=?
• ΔEk=260 (35)
• ΔEk=9100 J
Example
• A student pushes a 25 kg crate which is initially at rest with a force
of 160 N over a distance of 15 meters. If there is 75 N of friction,
what is the final speed of the crate?
• ΔEk=Fnetd
• Ek=1/2mv2
•
•
•
•
m=25 kg
F applied=160 N
d=15 m
Ff=75 N
Work, Energy, and Power
Conservation of Energy
Law of Conservation of Energy
•
•
•
•
•
Energy cannot be created or
destroyed, only converted into
other forms of energy
TOTAL energy is always conserved
Potential energy can be converted
to kinetic energy as an object
moves
When only conservative forces act
on object potential energy is
completely converted to kinetic
energy
When nonconservative forces like
friction act on an object, some
energy will be converted to heat
Mechanical Energy
• Mechanical Energy is the sum of kinetic energy and all forms of
potential energy associated with an object
• ME=KE + PE
• When only conservative forces act on an object then mechanical
energy is conserved
Law of Conservation of Energy (Quantitatively)
• Initial Energy= Final Energy
– Ei = Ef
– GPEi + Kei = GPEf + Kef
– mghi + ½ mv2i = mghf + ½ mv2f
• GPE=gravitational potential energy
Example
• A student falls from the building, if they reach the ground at 5.0
m/s , what height did they fall from?
•
•
•
•
•
Vf=5.0 m/s
Hi=?
Vi=0
Hf=0
GPEi + KEi= GPEf + KEf
Example
• While jumping over The Great Wall of China an 82 kg skateboarder
is needs to leave the ramp traveling at 22 m/s. A) How much
potential energy is needed to jump over? B) What minimum height
should the ramp be?
• m=82 kg
• Vf=22 m/s
• g=9.8 m/s2
• GPE=?
• h=?
• Ei=Ef
• GPEi + KEi= GPEf + KEf
• GPEi =Kef
• GPE = ½ mv2f
Clicker Question
• A 66 kg skateboarder jumps The Great Wall of China, clearly. At the
peak of jump he is 18 m high and traveling at 12 m/s . Assuming he
started at rest, find his initial height.
• A) 10 m
• B) 19 m
• C) 25 m
• D) 30 m
Clicker Question
• A 75 kg snowboarder slides up a frictionless rail to a height of
1.75m and slides across it at 2.50 m/s. How much kinetic energy
did he have before he went up the rail?
• A) 1520 J
• B) 1380 J
• C) 200 J
• D) Impossible to solve
Roller Coasters
• Although not perfectly energy efficient, they are a fun way to view
how work, gravitational potential and kinetic energy are exchanged
The Downhill skier
• When a nonconservative force is applied (friction)What’s this?
the work is negative because it is removing energy from the system
Work, Energy, and Power
Power
Power
•
•
•
•
Power (P) is the rate of doing work
Measured in J/s or Watts (W)
Power= Work/time
P=W/t
or P=ΔE/t
Clicker Question
• Mike performed 5 J of work in 10 seconds. Joe did 3 J of work in 5
seconds. Who produced the greater power?
• A) Mike
• B) Joe
• C) Both produced the same amount of power
Example
• Lover’s Leap is a 122 m vertical climb. The record time of 4 min 25 s
was achieved by Dan Osman (65 kg). What was his average power
output during the climb?
• h=122 m
• t=4 min 25 s  265 s
• m=65 kg
• g=9.8 m/s2
• P=?
• P=W/t or P= ΔE/t
Example
• A 1.00x103 kg car accelerates from rest to a velocity of 15.0 m/s in
4.00 s. Calculate the power output of the car. Ignore friction.
• m=1.00 x 103 kg
• Vf=15 m/s
• t=4.00 s
• P=?
• P=W/t or P=ΔE/t
Clicker Question
• A 68 kg student runs up a flight of stairs 3.2 m high in 4.8 seconds.
Determine their power output while running up the stairs.
• A) 217.6 W
• B) 45.33 W
• C) 440 W
• D) There is no work in this problem, not enough info
Clicker Question
• A 642 kg formula 1 car can reach a speed of 27.78 m/s in 1.7
seconds. What is the power output of the car during this
acceleration?
• A) 300,000 W
• B) 5000 W
• C) 150,000 W
• D) 3000 W
Another Useful Formula
• P=W/t
• P=Fd/t
– V=d/t
• So..
• P=FV
• Note this formula is only useful when the velocity is held constant
Example
• A student uses 140 N to push a block up a ramp at a constant
velocity of 2.2 m/s. What is their power output?
• F=140 N
• V=2.2 m/s
• P=?
• P=FV
• P=140 (2.2)
• P=310 W
Clicker Question
• An elevator motor has a power rating of 110 kW. How much force
would it exert if it was lifting a load at a constant velocity of 3.0
m/s?
• A) 3700 N
• B) 37 N
• C) 330 N
• D) 4 N
Work, Energy, Power
Efficiency
Efficiency
• A measure of how
much of the energy
that goes into a
machine actually gets
used
• Machines are useful
because they allow us
to use less force over a
longer distance to do
the same work
Efficiency of a Machine
• Eff= W out x 100
W in
• Eff= P out
P in
x 100
• There are no units for efficiency because it is a percentage
Example
A lever is used to lift a 50.0 kg object 10.0 cm. To do this
we must apply a force of 75 N to the end of the lever which
displaces 1.00 m. Find the efficiency of the lever
• What are the output variables?
• m=50.0 kg
• d=10.0 cm or 0.10 m
• What are the input variables?
• F=75 N
• d=1.00 m
Work, Energy, and Power
Thermal Energy
Thermal Energy Versus Temperature
• Thermal Energy or Heat
(q) - the total amount of
kinetic energy and
potential energy of the
particles in an object
• Temperature- The
average kinetic energy of
the particles in an object
• Temperature is an indirect
measurement of heat
• Which has more heat a
massive iceberg or a pot
of boiling water?
Changes in States of Matter
• All particles have kinetic energy
• Solids have the lowest amount of kinetic energy and gases (and
plasmas) have the highest amount of kinetic energy
• If heat is added to an object the molecules will gain kinetic energy
and as a result they will generally expand
Changes in States of Matter
• If an object is heated it will either
• 1) increase temperature
• 2)Change state in matter
Discussion Question
• Why is it better to leave sodas to cool in an ice chest of ice rather
than an ice chest of 0°C liquid water?
The Flow of Heat
• Heat always flows from
high to low
concentration by either
– Conduction
• Contact
– Convection
• Movement of fluid
– Radiation
• No medium required
• This transfer occurs
until thermal
equilibrium is achieved
Specific Heat Capacity
• Specific heat capacity is the amount of heat energy required to
heat 1 gram (or kg)of a substance by 1 °C
• What does it mean when a substance has a higher specific heat
capacity?
• The larger c is, the more energy required to heat the substance
Discussion Question
• Why is water a better choice to be used as a coolant instead of any
of the choices below?
Measurement of Heat
•
•
•
•
•
•
The amount of heat transferred to an object is found with
Q=mcΔt
Q=heat
m=mass
c=specific heat capacity (J/kg °C)
Δt=change in temperature (tf-ti) (°C)
Example
• Ms. K makes a cup of tea by boiling 250 g of water that is initially at
15° C. How much heat is needed?
• m= 250 g  0.250 kg
• Ti=0 ° C
• Tf=100 °C
• c=4180 J/kg °C
• q=?
• Q=mcΔt
• Q=(0.250)(4180)(100-15)
• Q=88825 J
Conservation of Heat
• Heat lost=heat gained
• If an object cools down the energy lost from this “hot” object is
gained from the surroundings
Example
• A 0.240 kg chunk of iron is heated to 215 oC and quickly placed into
0.275 kg of water that has a temperature of 12 oC. What will the
final temperature of the water be?
• Metal
• m=0.240 kg
• Ti=215 °C
• C=448 J/kg°C
• Water
• m=0.275 kg
• Ti=12°C
• C=4180 J/kg°C
• Tf=?
What is entropy?
• Entropy (ΔS)- measurement of disorder
• ΔS=Q/T
Q=heat T= temperature
• Entropy increases when heat is added to a substance, and
decreases when heat is removed
• Which has more entropy, a gas or a liquid?
• A gas
• What happens to the entropy as water freezes?
• The entropy of the water decreases since it becomes more ordered
and the entropy of the surrounding air increases
What is Internal Energy?
• Internal Energy (U) is the energy a substance has due to the motion
of the particles (kinetic energy) and the position of the particles
(potential energy).
Conservation of Energy
Predict the appearance of the bar graphs at points c, d, and e.
How are work and heat related?
• Energy can be converted into work or heat
• ΔU = Q + W