Transcript Work

Chapter 5
Work and Energy
Chapter Objectives
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Define work
Identify several forms of energy
Work-Kinetic Energy Theorem
Conservation of Energy
Power
Definition of Work
W = Fd
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Work is the product of the magnitudes of the component of a
force along the direction of displacement and the displacement.
Work is only done when the component of force is parallel to the
displacement.
The units of work is Newton (Force) x meter (displacement) =
Nm.
Work is a scalar quantity that can be negative or positive.
If the sign is positive, the force is in the same direction of the
displacement.
If the sign is negative, the force is in the opposite direction of
the displacement.
d
Θ
F
W = Fd cos Θ
Work is Confusing
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Work is only done when the force applied is
parallel to the displacement.
So carrying a bucket at constant velocity
does no work on the bucket.
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Notice constant velocity means that the net
force is 0.
Fa
No force, no work!
Fg
d
Types of Energy
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Kinetic energy is the
energy of an object due to
its motion.
Kinetic energy depends on
speed and mass.
The units for kinetic energy
is similar to work, so we
keep it different by using
Joule (J) for all types of
energy.
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K = 1/2mv2
Potential energy is the
energy associated with an
object due to the position
of the object relative to
some other location.
Potential energy is stored
energy.
Potential energy is present
in an object that has the
potential to move.
The units for potential
energy is the same for all
forms of energy, Joule (J).
Gravitational v Elastic Potential
Energy
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Gravitational potential
energy is the energy
associated with an object
due to the position of the
object relative to the Earth.
This based on the object’s
height above the Earth’s
surface.
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Ug = mgh
Elastic potential energy
is the potential energy in a
stretched or compressed
spring with the object at
rest.
This depends on the
distance the spring is
stretched or compressed.
It also depends on how
resistive the spring is to
being stretched or
compressed, called the
spring constant.
Us = 1/2kx2
Joule vs. Newton-meter
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The joule measures the same quantity as
the Newton-meter.
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The book will use joule for all
measurements, whether work or energy.
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So 1 J = 1 Nm
However, they list the Nm as the SI unit for
work?
So you can use either one and not be
penalized.
But, I would suggest (and prefer) that you
use
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Nm – Work
J – Energy (All Forms)
Other Forms of Energy
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Kinetic and both forms of Potential Energy fit into
the category of mechanical energy.
Mechanical Energy is any form of energy that
deals with motion.
Energy
Mechanical
Kinetic
Nonmechanical
Potential
Gravitational
Electrical
Elastic
Heat
Chemical
Why Joule?
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The joule is named for the British
Physicist James Prescott Joule (18181889).
Joule made major contributions to the
understanding of energy, heat, and
electricity.
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Law of Conservation of Energy
Joule’s Law
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That heat is produced in an electrical conductor.
Helped develop the absolute scale of
temperature while working with Lord Kelvin
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Kelvin Temperature Scale
Work vs. Energy
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Work and energy are linked by one common
concept
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They are measured in the same unit.
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1 joule (J) = 1 Newton-meter (Nm)
They are not only linked by their unit, but also
through their formula(s).
v2 = v02 + 2ad
ad = v2 – v02
W = Fd
W = mad
2
2–v 2
v
0
W=m(
)
2
W=
½mv2
–
½mv02
W = KE – KE0
W = ΔKE
Work-Kinetic Energy Theorem
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Remember that work is a measurement of the
force used to move an object a certain distance.
Since we are talking about motion, we must also
think of kinetic energy.
The units on both of them are similar; Joule - Nm
(which are the same things!)
Ultimately we can say that the net work done on
an object is equal to the change in kinetic
energy of the object.
That is the Work-Kinetic Energy Theorem.
Fd = Wnet = ΔKE = ½mv2 – ½mv02
Conservation of Energy
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Thanks to Albert Einstein’s observations about
energy being related to the amount of mass of
an object (E=mc2), energy is conserved
because mass is conserved.
That doesn’t mean the energy stays the same,
just the total amount remains constant, it just
changes form.
Mechanical energy is conserved as long as
friction is not present.
If friction is present, then some energy is
converted to heat, which is nonmechanical.
Conservation Equation
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You need to identify the initial condition of
the object and its final condition.
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Each situation may contain more than one type
of energy at the same time
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For instance, a parachutist jumping from an airplane.
All the energy from the initial condition
must be accounted for in the final
condition.
U0 + KE0 = U + KE
So
mgh0 + ½kx2 + ½mv02 = mgh + ½kx2 + ½mv2
If any of the three types of energy are not present, just
eliminate that type from the correct location in the
equation.
Power
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So what happens when two people do the same
amount of work, but one does it faster than the
other? Which person is better or stronger?
Power is the rate at which work is done. Also the
rate at which energy is transferred.
So machines with different power ratings do the
same amount of work in different time intervals.
Power is measured in joules per second, which is
called a Watt.
P=
W
Δt
Fd
=
Δt
But remember
that W = Fd.
= Fv
But remember
that d/Δt = v.