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WORK
AND
ENERGY
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Work is defined as a force that moves
through a distance. The equation used to
calculate work is: W=f d
If the 60kg cart is moved 20m to the right by a
force of 300N, the work done to move the cart
this distance is:
W=fd
W=300N x 20m
W= 6000Nm
Here is another situation in which work is done
against gravity.
Here the cart is pulled or pushed up a hill to a height of 20m. The
force being lifted is the weight of the cart. So if we are to determine
the work done we must first determine the weight of the cart.
Fw = mag
W = fd
Fw = 60kg x 9.80m/s2
W= 588N x 20m
Fw = 588N
W=11760Nm
ENERGY is defined as the capacity to do
work.
There are many forms of energy, but two
important forms are Kinetic energy and
Potential energy. Kinetic energy is the
energy possessed by moving masses. Kinetic
energy depends on both the objects mass
and the objects velocity.
KE= 1/2mv2
The 60kg cart has a velocity of 3.0m/s. The
cart’s Kinetic energy is:
KE=
½
mv2
KE= ½ 60kg x (3.0m/s)2
KE= 270Nm or 270Joules
( 1 Joule is equal to 1Nm)
Potential energy is energy that is stored
and is available for use at some time in
the future. There are a number of forms
of potential energy…One form is
Gravitational Potential Energy. GPE is the
energy that is stored by an object
because of its position above a surface.
Remember the cart that climbed the hill?
The gravitational potential energy stored by the
cart when it is at the top of the hill is determined
using the equation
GPE=mgh
GPE=mgh
GPE=60kg x 9.80m/s2 x 20m
GPE= 11760Joules
Doing work requires energy. In a real sense this means
that energy and work are always equal to each other.
When work is done moving a force through a distance,
energy is consumed.
W = fd
W= 588N x 20m
W=11760Nm
GPE= mgh
GPE = 60kg x 9.8m/s2 x 20m
GPE = 11760Nm or 11760 Joules
Note that the work
done and the energy
stored are the same.
Energy is conserved. This means that energy is
never destroyed or lost, it only changes from one
form to another. Here is an example of how this
happens.
When the barrel is rolled to the top of the ramp the GPE
stored is:
GPE=mgh
GPE= 30kg x 9.80m/s2 x 3.0m
GPE= 882 J
When the barrel falls off the top of the ramp the
GPE is changed into Kinetic energy and then into
heat and sound
The energy is CONSERVED.
The Law of Conservation of
Energy states that energy is
conserved. It is never lost or
destroyed, it simply changes from
one form to another.
Practice what you have learned
(A “GPE” problem…)
A 2.0kg pendulum swings to a height of 3.0m above its
resting position. How GPE does it have at this height?
GPE= mgh
GPE= 2.0kg 9.8m/s2 3.0m
GPE= 58.8J
Remember 1Nm = 1Joule
(Another WORK DONE AGAINST GRAVITY
problem)
A 75kg carpenter climbs to the top of 4.0m ladder.
How much work has he done?
W=fd
W= ( weight) distance This is because his work
is done against gravity.
W= (m g) d
W= (75kg 9.8m/s2) 4.0m
W= 2940Nm or 2940J
( A Work / energy theorem problem.)
A 75kg carpenter climbs to the top of 4.0m ladder. How
much work has he done?
GPE=mgh
GPE=75kg 9.8m/s2 4.0m
GPE= 2940J  ***The answer is the same as the
previous problem: Work done = energy gained***
(Work done by a force other than gravity…)
A. What is the force shown in the diagram below?
F=200N
B. How far did Moe push the Refrigerator?
10m
C. How much work did he do pushing the refrigerator?
W=fd
W= 200N 10m
W= 2000J
(A kinetic energy problem…)
What is the kinetic energy of the .30kg ball shown
here?
KE=1/2mv2
KE= ½ .30kg (20m/s)2
KE= 60J
The End…for now