Work and Energy

Energy and Work

• ENERGY is the capacity for doing work.
• In physics, work is defined as a force acting upon an
object to cause a displacement
• WORK = FORCE × DISPLACEMENT
W = Fx
• In order for a force to qualify as having done work on
an object, there must be a displacement and the
force must cause the displacement
• Unit: Newton x meter = Joule
• Work and energy have the same units.
 Work??
• Are the following examples of work as its
defined in physics?
a) A teacher applies a force to a wall and becomes
exhausted.
b) A book falls off a table and free falls to the
ground.
c) A waiter carries a tray full of meals above his head
by one arm across the room.
d) A rocket accelerates through space.
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/energy/au.html
 Work?
a) No, the wall does not move, there is no
displacement.
b) Yes, the force of gravity causes the book to fall
c) No, there is a force, the waiter pushes up on the
tray but this force does not make it move
horizontally. If the force and displace 90 degrees
(perpendicular) then no work is done.
d) Yes, there is a force that accelerates the rocket. If
the rocket was moving at a constant velocity, there
would be no work, because no force would be
needed to keep it moving at a constant velocity.
 Work Questions
1) A 10-N forces is applied to push a block
across a friction free surface for a
displacement of 5.0 m to the right.
a) Which forces are doing work on the block?
b) Find the amount of work done by each force.
2) How much work is done by an applied
force to lift a 15-Newton block 3.0
meters vertically at a constant speed?
3) Challenge: A tired squirrel (mass of 1 kg)
does push-ups by applying a force to
elevate its center-of-mass by 5 cm.
Determine the number of push-ups
which a tired squirrel must do in order to
do a mere 5.0 Joules of work.
 Power
Power = rate of doing work
= rate of delivering energy
W
P=
t
Units: Watt = Joule/second (SI units)
Other units for power: Horsepower = 550 ft-lb/s = 746 Watts
 Work and Power Triangle

W W
P=
P t
t

WORK = FORCE × DISPLACEMENT

W = Fx
P P = Fv W

F v F x
 Work and Power Questions
1) Two physics students, Will and Ben, 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? ______________ Explain your answers.
2) 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? _____________
Explain your answers.
3) A tired squirrel (mass of approximately 1 kg) does push-ups by applying a
force to elevate its center-of-mass by 5 cm in order to do a mere 0.50
Joule of work. If the tired squirrel does all this work in 2 seconds, then
determine its power.
4) 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?
 Mechanical Energy
• Energy is defined as the capacity to do work.
• Performing work on an object may give it the
capacity to do work, and therefore energy (e.g.
winding up a spring or raising a pile driver).
• Mechanical energy is defined as the energy of
an object due to its position or motion, or both.
 Potential Energy
• The energy of an object due to its position relative to
other objects is called potential energy (PE).
• Gravitational potential energy is the energy stored
in an object as the result of its vertical position
relative to the surface of the Earth or other object.
Gravitational potential energy = weight  height
PE = mgh
 Kinetic Energy
• The energy of an object due to its motion is
called kinetic energy.
1
Kinetic energy = mass  velocity2
2
1 2
KE = mv
2
• Kinetic energy is the other component of
mechanical energy. In this class, we will define
total energy as kinetic plus potential but there
are other kinds of energy. TE = PE + KE
• http://www.brainpop.com/science/energy/kineticenergy/
 Conservation of Energy
• Energy can neither be created nor
destroyed.
OR

• The total amount of energy in an isolated

system never changes.
Energy simulation: http://phet.colorado.edu/web-pages/simulations-base.html

In physics, energy conservation means energy

may be transformed from one form to
another, or to work, with no net loss or gain.
 Transformation of energy
• PE is transformed into KE, then some goes back to
PE, and back again and so on. If there is no friction,
the total amount of energy (KE + PE) does not
change. Total is always 40,000 J
 More transformation of energy examples
• http://www.physicsclassroom.com/mmedia/e
nergy/pe.html

• http://www.physicsclassroom.com/mmedia/e
nergy/ce.html
 Energy Questions
1) In the following specify if the energy is changing from PE to KE or KE
to PE. Explain each answer.
a) A ball falls from a height of 2 meters in the absence of air resistance.
b) A baseball is traveling upward towards a man in the bleachers.
c) A bungee chord begins to exert an upward force upon a falling bungee jumper.
2) In the following specify if there is a change in PE, KE or both. Explain
each answer.
a) Rusty Nales pounds a nail into a block of wood. The hammer head is moving
horizontally when it applies force to the nail.
b) A weightlifter applies a force to lift a barbell above his head at constant speed.
3) An object which weighs 10 N is dropped from rest from a height of 4
meters above the ground. When it has free-fallen 1 meter its total
mechanical energy with respect to the ground is
4) During a certain time interval, a 20-N object free-falls 10 meters.
The object gains _____ Joules of kinetic energy during this interval.
5) Determine the kinetic energy of a 1000-kg roller coaster car that is
moving with a speed of 20.0 m/s.
 Work-Energy Theorem
• The kinetic energy gained or lost by an object
is equal to the work done by a net force acting
on the object. Net work =  KE

Fx =  KE
• The work- energy tells that when a car’s speed
doubles, it will skid 4 times as far when
stopping
• Example of work-energy theorem and its
applications:
– http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/energy/se.ht
ml
– http://www.physicsclassroom.com/mmedia/energy/hw.html
– http://www.physicsclassroom.com/mmedia/energy/cs.html
 Simple Machines
• A machine is defined as a
device that can increase,
decrease or change the
direction of the applied
force.
• A simple machine has few or
no moving parts.
• Simple machines do not
increase work done, energy
output or power, they can
only change increase output
force.
 Machines –lever and pulley
• Machines like levers and pulleys multiply forces
or change the direction in which forces act.
Lever Pulley

• The lever and the pulley enable a smaller force

to be applied through a larger distance to yield
an equivalent amount of work.
 Types of levers
• In a first class lever the
fulcrum is in the middle and
the load and effort is on
either side. Example: see-saw
• In a second class lever the
fulcrum is at the end, with
the load in the middle.
Example: wheelbarrow
• In a third class lever the
fulcrum is again at the end,
but the effort is in the
middle. Example: tweezers
 Machines – inclined plane
• Another example of a simple machine is an inclined
plane, or ramp.
• When doing work, this type of slanted surface
reduces the force you need to exert on something.
• For an ideal inclined plane, where there is no loss
due to friction:
applied force  applied distance = output force  output distance
Work to push up ramp (1 N)(6 m) = (3 N)(2 m)
Work to lift straight up
1N
W = (6 m)(1 N)

W = (2 m)(3 N) 2m 6m
 Why Use Simple Machines?
• We use simple machines for the
mechanical advantage. Even simple
machines can offer a significant
increase in output force.
• Mechanical advantage can be thought
of as the number of times a machine
multiplies the applied force. It is the
ratio of applied force to output force.
For machines that increase output
force, MA is greater than one.

output force applied distance

MA = =
applied force output distance
 Efficiency of Energy Conversion
• In ideal machine, the work output equals the
work input (efficiency is 100%). There are no
ideal machines.
• All real machines convert some work to heat
through friction (efficiency is less than 100%).
useful energy output
Efficiency = 100%
total energy input
• An automobile has an overall efficiency of 15-
20% (80-85% is waste heat due to friction, to
the cooling system or carried off by exhaust
gases).
 Finding efficiency and MA for a ramp
• If the ramp is not 100% efficient, extra force will be required
to push box up the ramp
• Useful energy output is the energy required to lift the box
straight up
• Total energy input is the energy required to push the box up
the ramp.
• e = 6 J/12J x 100% = 50% (efficiency always less than 100%)
• MA = 3 N/2 N (MA is usually greater than 1)
2N
W = (2 N)(6 m)

W = (3 N)(2 m) 6m
2m
 Machine Questions
1) What do machines do?
2) Try to figure out the MA and efficiency of this inclined
planes:
60 N

1500 N

3) Try to figure out the MA and efficiency of this pulley system:

12 N A 12 N force is required to pull the 20 N
bucket straight up. When the rope is
pulled down 4 m, the bucket rises 2 m.

20 N
 Machine Questions cont.
4) What effort force is required to lift a person on this lever?

5) An ideal lever 5 meters long is used to lift up a load of 1000 N.

The lever gives a mechanical advantage of 4. Sketch the lever
and show the location of the fulcrum and the forces at each
end of the lever.
 Sources
• Conceptual Physics by Paul Hewitt
• www.physicsclassroom.com
• http://rigel.physics.unr.edu/faculty/phaneuf/c
lassinfo/index100.html
• www.generalpatton.org/education/lesson_pla
ns/Simple_machines.ppt