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# PH 121 11.1-11.2

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## Richard Datwyler

on 29 June 2015

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#### Transcript of PH 121 11.1-11.2

Work
What is work?
How would you define it?
Expanding our energy model.

When we began energy we played with the idea
of money being conserved.

The person had a job and that brought money in
he had expenses and that took money out

In physics the process of bringing energy into or out of a system is work.
If work is done on the system, W > 0 and it is brought in

If work is done by the system, W < 0 and is taken out.
Also our little parable, only had one type of energy, Mechanical
He transferred his savings (potential) to liquid (kinetic) energy.

Mechanical isn't the only type of energy.
There is an internal energy of the motion of each atom, this is a
thermal energy, it has to do with temperature.

Thus we define energy of a system now as:
With this addition of thermal energy we can transfer our total
energy around a bit more.
We can explain why a book comes to rest.
The initial kinetic energy, got turned into thermal energy.
It heated up the atoms.
As we consider our basic model of energy we now can discuss decreases to our system, Not just straight conservation inside the system.
Looking at this. We can say energy is transferred in
to our system if W is positive. (out if negative)
and
Energy is transformed in our system if W is zero.
Think back to the text book on table.
Tell me what happens to each of these terms and
what does that mean for my system.

Can you think of a similar example with Work being
the opposite sign?
Work and Kinetic Energy
Your book gives you 7 great definitions
2 job
4 work of art
5 Steel works
6 works (how things operate)
7 Transfer of energy to a body by application of a force
When we derived conservation of kinetic and potential energy of gravity and a spring we played around with Newton's 2nd law, and partial differentials. We'll do the same here.
This last term we will use as a definition
'how much energy does work transfer'
From these two equations together we can get a definition of work.
Note this was just one force in one direction
If we add up all forces and directions we get the following
Not a lot of change, but important none the less. This is the
Work-Kinetic Energy theorem.
One of the questions that we might have thought about
as we began this section on energy was:
"how does a system gain or lose energy"

A system gains or loses kinetic energy when work transfers
energy between our system and the environment.
Now there is a really cool analogy

We have two definitions of Work:
This looks similar to Impulse
momentum theory
Looking at them close we see that a force acting on a system will change the state of the particle.
If the force is done over a time, it changes the momentum,
if it is done over a distance it changes the kinetic energy.
This does not mean that the force either does one or the other.
Either changing the momentum or the energy.
It actually does both, the question is how we look at it.
Consider a car race
Same force
a= F/m
B will accelerate more
After Some amount of
Time = t1
B will be winning
But their momentum's
will be the same.
When they both finally finish the race
B will have gotten there first

But over the same distance their Kinetic
energies will be the same
If this idea is true, there must then be some
way of comparing momentum to energy.
When the Kinetic energies
are the Same

Smaller mass smaller Momentum
When both Momentum's
are the same

Smaller mass Larger Energy
Also note, the integral-area concept
All right.
now that we have had some fun comparing
these two theorems
Let us get back to work.

Example

How much work is done to slow a
1500 kg car from an initial speed of 35 m/s
to rest?

919 KJ
Evaluate the dot product A*B if

a. A = 4i - 2j B = -2i - 3j
b. A = -4i +2j B = 2i +4j
What is the angle between the vectors A and B for both parts a. and b. ?
-2
0
90
97
"why does the normal force exert zero work?"
"How can we use work to show how much energy is lost in a system?"
"Can we have a little review about the differences between momentum, energy and work? "
"Can we do an example of a dot product?"
"What is the difference between power and work?"
"Could you explain net work (Wnet)?"
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