Potential Energy - Mona Shores Blogs
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Transcript Potential Energy - Mona Shores Blogs
Chapter 5
Work and Energy
Chapter Objectives
Define work
Identify several forms of energy
Work-Kinetic Energy Theorem
Conservation of Energy
Power
Definition of Work
W = F(x)
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.
x
Θ
F
W = F(x) cos Θ
Work is Confusing
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.
Notice constant velocity means that the net acceleration is 0.
If net acceleration is 0, then net force is 0.
Fa
No force, no work!
Fg
x
Types of Energy
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.
KE = 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
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.
PEgravitational = 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.
PEelastic =
1/ kx2
2
Joule vs. Newton-meter
The joule measures the same quantity as the
Newton-meter.
So 1 J = 1 Nm
The book will use joule for all measurements,
whether work or energy.
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
Nm – Work
J – Energy (All Forms)
Other Forms of Energy
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?
The joule is named for the British Physicist
James Prescott Joule (1818-1889).
Joule made major contributions to the
understanding of energy, heat, and electricity.
Law of Conservation of Energy
Joule’s Law
That heat is produced in an electrical conductor.
Helped develop the absolute scale of temperature
while working with Lord Kelvin
Kelvin Temperature Scale
Work vs. Energy
Work and energy are linked by one common concept
They are measured in the same unit.
1 joule (J) = 1 Newton-meter (Nm)
They are not only linked by their unit, but also
through their formula(s).
vf2 = vi2 + 2ax
ax = vf2 – vi2
W = Fx
W = max
2
2 – v2
v
i
W=m( f
)
2
W=
½mvf2
–
½mvi2
W = KEf - KEi
W = ΔKE
Work-Kinetic Energy Theorem
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.
Fx = Wnet = ΔKE = ½mvf2 – ½mvi2
Conservation of Energy
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
You need to identify the initial condition of the object
and its final condition.
Each situation may contain more than one type of energy at
the same time
For instance, a parachutist jumping from an airplane.
All the energy from the initial condition must be
accounted for in the final condition.
So
PEi + KEi = PEf + KEf
mghi + ½kx2 + ½mvi2 = mghf + ½kx2 + ½mvf2
If any of the three types of energy are not present, just
eliminate that type from the correct location in the
equation.
Power
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
F x
=
= Fv
Δt
But remember
that W = Fd.
But remember
that d/Δt = v.