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```					Work and Energy

Unit 5
Work

• Issues talked about have the same meaning in
everyday life as they do in physics
• In everyday life, work means to do something
that takes physical or mental effort
• In physics work has a different meaning
 Ex: holding a heavy chair at arms length for several
minutes
 No work is done on the chair
 Ex: carry a bucket of water along a horizontal path
while walking at constant velocity
 No work is done on the bucket
Work

• Work is done on an object when a force causes
a displacement of the object
• Work-the product of the component of a force
along the direction of displacement and the
magnitude of the displacement
 W=Fd
 Where W is work, F is force, and d is displacement
 Work is not done on an object unless the object is
moved with the action of a force
 The object must move otherwise no work is done on the
object
Work

• Work is done only when components of a force
are parallel to a displacement
 Components of the force perpendicular to a
displacement do not do work
 If I push on a crate on a horizontal surface at an
angle, , below horizontal, only the horizontal
component of the force causes a displacement and
contributes to the work
 W=Fd cos()
 If many forces are acting on an object, you can find
the net work done by finding the net force on the
object first
 Wnet=Fnetd cos()
Work

• Work has dimensions of force times length
 Units for work
 1 Nm=1J
 1 joule of work is about the amount of work needed
to raise an apple from your waist to the top of your
Work

• The sign of work is important
 Work is a scalar quantity and can be positive
or negative
 Work is positive when the component of force is in
the same direction as the displacement
• Also for when an object speeds up
 Work is negative when the force is in the direction
opposite the displacement
• Ex: kinetic friction, work done by friction is negative
• Also for when an object slows down
Work

• Ex: How much work is don on a vacuum
cleaner pulled 3.0 m by a force of 50.0 N
at an angle of 30.0 degrees above the
horizontal?
Energy

• Kinetic energy-the energy of an object that is
due to the object’s motion
 Kinetic energy depends on speed and mass
 KE=(1/2)mv2
 Mass is measured in kg, velocity in m/s
 Kinetic energy is a scalar quantity and is measured in
units of joules
 If a bowling ball and a volleyball are traveling at the
same speed, which do you think has the grater kinetic
energy?
Energy

• Ex: A 7.00 kg bowling ball moves at 3.00
m/s. How fast must a 2.45 g table tennis
ball move in order to have the same
kinetic energy as the bowling ball? Is this
speed reasonable for a table-tennis
player?
Energy

• The net work done on a body equals its change
in kinetic energy
 Work-kinetic energy theorem - the net work done by
all the forces acting on an object is equal to the
change in the object’s kinetic energy
 Wnet=KE
 Wnet=(1/2)mvf2-(1/2)mvi2
 When using this theorem, you must include all the forces that
do work on the object in calculating the net work done
 The work-kinetic theorem allows us to think of kinetic energy
as the work that an object can do while the object changes
speed or as the amount of energy stored in the motion of an
object
Energy

• Ex: On a frozen pond, a person kicks a
10.0 kg sled, giving it an initial speed of
2.2 m/s. How far does the sled move if the
coefficient of kinetic friction between the
sled and the ice is 0.10?
Energy

• Potential Energy-the energy associated
with an object because of the position,
shape, or condition of the object
 Potential energy is stored energy
 Associated with an object that has the potential to
move because of its position relative to some other
locations
 Depends on properties of the object and its
interaction with its environment
Energy

• Gravitational potential energy-the potential
energy stored in the gravitational fields of
interacting bodies
 Gravitational potential energy depends on height from
a zero level
 PEg=mgh
 Only for when free-fall acceleration is constant over the entire
height
 Zero level can be arbitrarily set
 Ex: marble falls off a table
 Potential energy is converted to kinetic energy
Energy

• Elastic potential energy-the energy available for
use when a deformed elastic object returns to its
original configuration
 Elastic potential energy depends on distance
compressed or stretched
 Ex: a spring
 The length of a spring when no external forces are acting on it
is called the relaxed length of the spring
 When an external force compresses or stretches the spring,
elastic potential energy is stored in the spring
 PEelastic=(1/2)kx2
 Where k is called the spring constant and x is the distance the
spring is compressed or stretched
Energy

• Ex: A 70.0 kg stuntman is attached to a bungee
cord with an unstretched length of 15.0 m. He
jumps off a bridge spanning a river from a height
of 50.0 m. When he finally stops, the cord has a
stretched length of 44.0 m. Treat the stuntman
as a point mass, and disregard the weight of the
bungee cord. Assuming the spring constant of
the bungee cord is 71.8 N/m, what is the total
potential energy relative to the water when the
man stops falling?
Conservation of Energy

• The description of the motion of many
objects often involve a combination of
kinetic and potential energy as well as
different forms of potential energy
 Ex: pendulum clock
 At the highest point of its swing, there is only
gravitational potential energy associated with its
position
 At other points in the swing, the pendulum has
motion so it has kinetic energy as well
Conservation of Energy

• We can ignore other forms of energy (I.e.
chemical, heat, etc.) if their influence is
negligible or if they are not relevant to the
situation being analyzed
• Mechanical Energy-the sum of kinetic energy
and all forms of potential energy
 ME=KE+PE
 Nonmechanical energy types: nuclear, chemical
internal, and electrical
 MECHANICAL ENERGY IS NOT A UNIQUE FORM
OF ENERGY. IT IS ONLY A WAY OF CLASSIFYING
ENERGY!
Conservation of Energy

• Mechanical energy is conserved
(assuming no friction)
 Conserved means is converted between
different forms, but not lost
 The total potential energy and kinetic energy
of an object will be the same anywhere along
its path
 MEi=MEf (in the absence of friction)
 Depends on the forms of potential energy
 (1/2)mvi2+mghi=(1/2)mvf2+mghf
Conservation of Energy

• Energy conservation occurs even when
acceleration varies
 We can apply a new method of solving
problems because of this instead of worrying
 We set up the initial mechanical energy equal
to the final mechanical energy and ignore the
information in between
Conservation of Energy

• Mechanical energy is not conserved in the
presence of friction
 Total energy is always conserved
 However, when friction is involved, the
mechanical energy is converted into forms of
energy that are much more difficult to account
for
 Therefore that energy is considered to be “lost”
Conservation of Energy

• Ex: Starting from rest, a child zooms
down a frictionless slide from an initial
height of 3.00 m. What is her speed at the
bottom of the slide? Assume she has a
mass of 25.0 kg.
Power

• Power-a quantity that measures the rate at
which work is done or energy is
transformed
 P=W/t
 An alternate form is substituting W=Fd into
the equation
 P=Fd/t
 d/t is another way of writing the speed of an
object
 P=Fv
Power

• SI unit is the watt, W
 One joule per second
 Horsepower is another unit of power
 1 hp=746 watts
Power

• Ex: A 193 kg curtain needs to be raised
7.5 m, at constant speed, in as close to
5.0 s as possible. The power rating for
three motors are listed as 1.0 kW, 3.5 kW,
and 5.5 kW. Which motor is best for the
job?

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