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Following points are the summary of these Lecture Slides : Understanding Work, Hold, Exerting, Force, Doing Work, Distance, Consideration, Pole Exerts, Moving Ball, Tether Ball
Typology: Slides
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When you hold something, are you
exerting a
force
on the object?
Yes
When you hold something, are you
doing
work
If you set the object on a table, does the
table
exert a force
on the object?
Yes
. Does the
table do any work
No
When you hold something, then,
you are not
doing work either
What can you do that the table can’t do? You
can lift the object up - which is work! We define the concept of
as the
exertion of
force through a distance
There is one more consideration, however. In
tether ball, the pole exerts a force on themoving ball (via the rope).
Does the pole
do work?
The
difference
is in the
direction
. The pole
was pulling on the tether ball perpendicularto the motion of the tether ball. The playerwas pushing on the tether ball in the samedirection as the motion. In part two, however, we also had torque as
being force across a distance. What is thedifference?
In applying torque, the direction of the force
had to be perpendicular to the distance.This caused a turning force:
= r F sin(
rF
In doing work, the direction of the force has to
be parallel (or anti-parallel) to the distancemoved. We write this this way:
Work = F
s
where the dot indicates the cosine of the angle
between F and s:
Work = F s cos(
Fs
We can now define the concept of energy: Energy is the capacity to do work (in ideal
circumstances). We all know that we can do work: exert a
force through a distance. But to do thatrequires food. Thus we
convert
the energy
in food into work. The same thing happenswhen we
burn
coal to
generate
heat which
can be
converted
into electricity which can
be
converted
into lots of useful work.
Many such examples as we just saw lead us to
propose a natural
law
. Remember that a
natural law is a statement of how natureseems to work - it is not “derived” fromanything more basic, it is observed to fit theresults of observations (experiments). Energy can neither be created nor
destroyed (that is, energy is conserved).However, it can be transformed from oneform into another.
The units of energy (and work) are:
Nt*m =
Joule
A British unit of energy is the BTU (British
Thermal Unit).
1 BTU = 1,054 Joules
(This is the energy necessary to heat one pound of water 1
o F.)
Another unit of energy is the calorie.
1 calorie = 4.186 Joules
(This is the energy necessary to heat one gram of water 1
o C.)
However, the calorie we refer to when we
eat
is
really a
kilocalorie = 4,186 Joules
The units of
torque
are: Nt*m =
Ntm*
Note that even though torque and energy both
have units of Nt*m, they are differentquantities, and so they have different formalnames. Energy units are in Joules, whiletorque units are simply specified as
Ntm*
In the British system, the unit of torque is
simply called the foot-pound (
ft-lb
Energy of
motion
, called
Kinetic Energy
should depend on mass and speed of object.Your car has energy when it is moving.The wind has energy when it is moving, andwe can convert this wind energy intoelectric energy via windmills.
Energy of
position
, called
Potential Energy
should depend on why that position hasenergy. The water stored behind a dam has energy due to it’s
height above the base of the dam. We can use thisto run a hydroelectric station. The energy in foodis due to the molecular binding of the atoms in thefood. The same is true for coal, oil and gas.There is also energy stored in the nucleus of atoms- nuclear energy.
If we let an object fall, it gains speed. It also
gains what we call kinetic energy. By theConservation of Energy law, the amount ofwork going into the object (from gravity)will equal the amount of energy the objecthas (kinetic): F s cos(
) = mg h (1). But if
an object falls a distance h with anacceleration of g, how fast is it going?
KE(m,v) = mgh
(The amount of kinetic energy,
which depends on the quantities mass and speed inthis case equals the amount of work done bygravity, mgh). From our motion equations,
v = v
o^
+ gt
and
h = h
o^
+ v
t + (1/2)gto
2
or in this case (h
=0,o^
v
=0):o
h = (1/2)gt
2 , or t = (2h/g)
1/
so v = gt =
g(2h/g)
1/
, or v = (2hg)
1/
, or h = (1/2)v
2 /g; thus
mgh = mg(1/2)v
2 /g =
(1/2)mv
2
.
You’ve probably heard the expression: “speed
kills”. This comes from the fact that KEdepends on the square of the speed. If youdouble your speed, you quadruple theamount of energy of the object. Andremember that energy is the capacity to dowork - for either good or bad. Uncontrolledenergy can exert large forces throughsignificant distances - which can be verydangerous!
Note that the difference between (1 m/s)
2
and
(2 m/s)
2
is 3 m
2 /s
2 , whereas the difference
between (99 m/s)
2
and (100 m/s)
2
is 199
m
2 /s
2
. What this indicates is that it takes
more and more energy to move faster andfaster. This explains why there is so littledifference between first and tenth in a speedrace between trained athletes!
