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ENERGY
The ability to do work
ENERGY COMES IN MANY FORMS
A. MECHANICAL
B. ELECTRICAL
C. CHEMICAL
WORK: A force acting through a distance, in the
direction of the force.
Units; Joules, Nm, Btu, cal, ft-lb
Formulas:
a. W=Fxd
b. W=Fxdxcosq
c. W=FxrxDq
d. W=TxDq
Work is defined graphically by the area under the curve in a
graph that shows force as the independent variable and
distance as the dependent variable
Variable
Constant
A force can be exerted on an object and yet do no work.
W = F x d x cosQ
a. F is the force
b. d is the displacement
c. Theta is the angle between the force and the displacement vector.
and is associated with the amount of force which causes the
displacement.
1.
2.
3.
When determining the measure of the
angle in the work equation, it is important
to recognize that the angle has a precise
definition - it is the angle between the
force and the displacement vector.
If the force is applied parallel to the
incline, the displacement of the cart
is also parallel to the incline. Since F
and d are in the same direction, the
angle is 0 degrees
a. As long as the work done is parallel to the plane that the
object traverses, the cosQ will be 00.
b. If the plane that the object moves on is at an angle and
is frictionless, then Fnet is not (FwsinQ’- mFwcosQ’) but
will be FwsinQ’ ,there is nothing to resist the applied force.
c. As the plane increases the applied force increases
d. Because the plane reaches to a specific height, as the
angle of the plane increases the length of the plane
decreases.
e. Therefore, work remains the same for any mass that is
taken to a specific height along the surface of a frictionless plane
Apply the work equation to determine the amount of work done
by the applied force in each of the three situations described
below.
POWER
The quantity work has to do with a
force causing a displacement. Work
has nothing to do with the amount of
time that this force acts to cause the
displacement. Sometimes, the work is
done very quickly and other times the
work is done rather slowly
The quantity which has to do with the
rate at which a certain amount of work is
done is known as the power
The standard metric unit of power is the Watt
A Watt is equivalent to a Joule/second
One horsepower is equivalent to approximately 750 Watts
To be a powerful lineman you should be strong (apply
a large force) and quick (displacement occurs over a
short period of time).
A Walker
-work done is
large
-time is very
large
-power rating
would be small
A Rock
Climber
-work done
is large
- it takes
less time
than the
walker
- power
rating would
larger than
the walker
A Bicycler
- work done is
large
- it takes less
time than the
walker and rock
climber
- power rating
is larger than
the rock
climber
A student does 82 J of work when lifting her textbooks from the floor
to her desk. It took her 3.0 s to do this task. What is her power?
Solution:
Since work done is approximately equal to the energy used, W = ~E,
power can also be described as the rate at which energy is used.
To determine power produced by a moving object you must know its
force and average velocity.
Where,
Check Your Understanding
A 1.0 x 103 kg car accelerates from rest to a velocity of 15.0
m/s in 4.00s. Calculate the power ouput of the car in 4.00s.
All machines are typically described by a power
rating. The power rating indicates the rate at
which that machine can do work upon other
objects. Thus, the power of a machine is the
work/time ratio for that particular machine
Law of Conservation of Mechanical Energy:
-The sum of the potential and kinetic energy of an ideal energy
system remains constant.
Conservative Forces
Gravitaional and Elastic forces are
“conservative forces”
because they are responsible for
the exchange between
Potential and kinetic energy in simple
harmonic motion
Dissipative Forces
a. There are forces that produce deviations from the
law of conservation of mechanical energy.
b. Friction is an example of such a force.
c. These forces are called “nonconservative” or “dissipative.”
d. Friction is a dissipative force because it produces a form of
energy (heat) that is not mechanical.
e. Energy is lost
f. In view of the law of the conservation of energy there is truly
no loss in energy.
g. Another observation to distinguish between conservative and
dissipative forces is to note the relationship between the force
and the path over which it acts.
Potential Energy
Potential energy exists whenever an object which has
mass has a position within a force field. The most
everyday example of this is the position of objects in
the earth's gravitational field.
The potential energy of an object in this case is given by the relation:
PE = mgh
Gravitational Potential Energy Application
Hydroelectric power is generated this way.
As the water falls, it turns a turbine, which
pushes electrons around creating an electric
current.
Elastic Potential Energy
Anything that
can act like a
spring or a
rubber band
can have
elastic
potential
energy.
A rubber band
stores energy
when stretched
and releases it
as kinetic energy
Springs work the same way, but you
can either stretch or compress
them. Wind-up watches store
potential energy in an internal
spring when you wind them and
slowly use this energy to power the
watch.
Chemical Potential Energy
The amount of energy in a bond is
somewhat counterintuitive - the
stronger or more stable the bond,
the less potential energy there is
between the bonded atoms.
Strong bonds have low potential
energy and weak bonds have high
potential energy.
Lot's of heat and/or light energy is
released when very strong bonds
form, because much of the
potential energy is converted to
heat and/or light energy. The
reverse is true for breaking
chemical bonds. It takes more
energy to break a strong bond than
a weak bond. The breaking of a
bond requires the absorption of
heat and/or light energy.
PE = Energy (in Joules)
m = mass (in kilograms)
g = gravitational acceleration of the earth (9.8 m/sec2)
h = height above earth's surface (in meters)
KINETIC ENERGY:
-An object in motion has the ability to do work and thus can
be said to have energy.
-From the Greek kinetikos, meaning “motion”
a. In order to obtain a quantitative definition for kinetic energy, we
have to consider a particle mass “m” that is moving in a straight line
with an initial speed v1
b. To accelerate it uniformly to a speed v2, a constant net force F
is exerted on it parallel to its motion over distance d.
c. Then the work done on the particle is W=Fd
d. Apply Newton’s second law, F=ma
e. Subsitute v22= v21 + 2ad for a
f. Then we find W=Fd=mad=m(v22-v21/2d)d
or W=(.5)mv22-(.5)mv21
g. We define the quantity (.5)mv2 to be the translational kinetic
energy KE=(.5)mv2
WORK ENERGY THEOREM:
The work done on a particle by the net force acting on it is
equal to the change in kinetic energy of the particle.
W = DKE = 1/2mv22 – 1/2mv21
a. The left-hand term represents the net work done on the
particle.
b. The right hand side of the equation is the difference between
the final and initial kinetic energies.
c. If the work done on the particle is positive, then its kinetic
energy increases.
d. The theorem emphasizes that work, or equivalently energy,
is needed to set a particle in motion.
e. The theorem is valid for constant and variable forces.
http://www.saskschools.ca/curr_content/physics30/mech/lessonii_
2_1.html
http://www.physicsclassroom.com/Class/energy/U5L1e.html
http://chemsite.lsrhs.net/chemKinetics/PotentialEnergy.html