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ENERGY
Work
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Work Formula
• Work = Force x Distance
W=Fd
• Factor one: there must be a force
applied
• Factor two: there must be movement in
the direction of the force
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Types of Work
• 1. The work done to
overcome a force (lifting
something to overcome
the force of gravity…)
• 2. Changing something’s
velocity (working against
its inertia to speed up or
slow down).
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Units
• Work – joules (J)
m
–a joule is a N•m or kg  2  m
s
• 1 J is the amount of work done by
1 N of force for 1 m of distance.
–For large work values we use kJ
(kilojoules, or 1000 joules).
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Power
• When we look at time we use power.
Power=
Work done
time interval
• The unit for Power is the Watt (W)
• 1 watt is the power expended when 1 Joule of work
is done in 1 second of time
– One kW (kilowatt) is 1000 watts. One MW (megawatt) is
one million watts
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Problems - 1
Adam, a very large man of mass 130 kg, stands on a pogo
stick. How much work is done as Adam compresses the
spring of the pogo stick 0.50 m?
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Problem - 2
After finishing her physics homework, Kayla pulls her 50.0 kg body
out of the living room and climbs up the 5.0-m-high flight of stairs to
her bedroom. How much work does Kayla do in ascending the stairs?
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Problem - 3
In the previous example, Kayla slowly ascends the stairs, taking 10.0
seconds to go from bottom to top. The next evening, in a rush to
catch her favorite TV show, she runs up the stairs in 3.0 seconds.
a) On which night does Kayla do more work?
b) On which night does Kayla generate more power?
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PRACTICE
PROBLEMS
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Energy
• Energy enables work to be done
• Mechanical energy is energy that comes from the
position of something or the movement of something
and it can be either potential energy or kinetic
energy
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Potential Energy
• Potential energy is energy due to position
• Chemical potential energy is found in food, fossil fuels, and electric
batteries.
• Positional potential energy can be found in a compressed spring, a
the string on a bow ready to shoot an arrow, etc.
– PE in this case equals the force times the distance used to store the
energy (how hard you pulled on the string times how far back you pulled
it.
• Gravitational potential energy comes from an objects distance from
the surface of the earth.
– Gravitational potential energy can be found by GPE = mgh (mass times
acceleration due to gravity times height)
– Gravitational potential energy only depends on height not on path
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Potential Energy Problems - 1
Legend has it that Isaac Newton “discovered” gravity when
an apple fell from a tree and hit him on the head. If a 0.20-kg
apple fell 7.0 m before hitting Newton, what was its change in
PE during the fall?
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Potential Energy Problems - 2
Legend has it that Galileo dropped objects off the Leaning Tower of
Pisa to determine whether heavy or light objects fall faster. If Galileo
had dropped a 5.0-kg cannon ball to the ground from a height of 12 m,
what would have been the change in PE of the cannon.
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Kinetic Energy
• Kinetic energy is energy of motion.
• KE = ½ mv² where m is mass and v is velocity or speed
• Kinetic energy is also equal to the amount of work done
to give the object the velocity that it has
• So…net force x distance = kinetic energy, which can also
be written as: Fd = ½ mv²
• Note that the speed of the object is squared; this means that if you
double the objects speed you are quadrupling the kinetic energy.
Also an object moving twice as fast takes four times as much work to
stop.
• The work energy theorem states that whenever work is
done energy changes. This can be represented by the
following formula: Work = E
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Kinetic Energy Problem - 1
A greyhound at a race track can run at a speed of 16.0 m/s.
What is the KE of a 20.0-kg as it crosses the finish line?
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Kinetic Energy Problem - 2
The 2000 Belmont Stakes winner, Commendable, ran the horse race at
an average speed of 15.98 m/s. If Commendable and jockey Pat Day
had a combined mass of 550.0 kg, what was their KE as they crossed
the finish line?
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PRACTICE
PROBLEMS
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Conservation of Energy
• The law of conservation of energy states:
Energy cannot be created or destroyed. It
can be transformed from one form into
another, but the total amount of energy
never changes.
– In order to see this we will need to look at
entire systems, not single objects!
– One of the classic PHYSICS examples of this
is the pendulum.
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Pendulum
• In this image you can
see that when the
pendulum is all the
way up, it has large
PE, when it has fallen
it has small PE, and
then when it rises
back up it has large
PE again
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More Pendulum
• Here you can see that when the pendulum is up
it has 10 J of PE and 0 KE and when it is down it
has 0 J of PE and 10 J of KE
• Disregarding friction,energy changes between
the two types but is not lost.
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Roller Coaster
• The rollercoaster is a more complicated
example, however you can see that at the top
there is 40,000 J of PE and 0 KE, and at the
bottom there is 0 PE and 40,000 J KE.
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The Energy Ramp
• In the energy ramp we can demonstrate the fact
that the path an object takes does not determine
its energy.
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Machines
• A machine is a device used to multiply forces or
simply change the direction of forces. Some
common simple machines are the:
– Lever
– Pulley
– Inclined plane
– Wedge
– Screw
– Wheel & axle
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The Lever
– The lever – we work on one end of the lever the other
end works on the load.
– Neglecting friction, work input equals work output. So
(force x distance) input = (force x distance) output.
( F  d )input  ( F  d ) output
• Fulcrum is middle point of lever
• Mechanical Advantage is ratio of input force to output force or
input distance traveled to output distance traveled.
• http://www.cosi.org/files/Flash/simpMach/sm1.swf
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The Pulley
– The Pulley – a pulley is a type of machine that
can be used to change the direction of a
force.
– The mechanical advantage of a simple pulley
system is the same as the number of strands
of rope that support the load. Note: Not all
strands on a pulley are necessarily
supporting!!!
http://www.cosi.org/files/Flash/simpMach/sm1.s
wf
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The Ramp
• The mechanical advantage of a ramp can
be found either by the ratio of input force
to output force or by the ratio of distance
traveled along the ramp to height risen.
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