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# PH 121 11.5-11.9 S15

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## Richard Datwyler

on 30 June 2015

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#### Transcript of PH 121 11.5-11.9 S15

Last of the WORK before the test
We are going to move to Thermal energy.

Just to clarify. When we say macroscopic, we are
speaking of motion, and dynamics of the object
Microscopic will be motion of atoms
On a macroscopic scale we have been discussing
potential energy (gravity and spring) and
Kinetic energy.
These two together gave us mechanical energy
Now we need to dive in to the object and see what
happens inside.
Following your text, consider a .5 kg block of iron
moving at 20 m/s
It has an amount of macroscopic kinetic energy
But it also has internal energy
Here you can
visualize both
types of energy
on a microscopic
level.
If we consider this same .5 kg piece of iron,
Iron has a molecular weight of 56 g /mole
so this gives us 8.9 moles then each mole
has Avogadro's number of atoms, giving
~ 5.4 x 10^24 atoms

So the mass of one atom is .50/5.4x 10 ^24
or about 9x 10 ^-26 kg
That is a fine mass, but what about the velocity

A bit hypothetical, but we know the speed of sound to be about 343 m/s in air, much higher in solids but for easy math lets say v = 500 m/s. This give a microscopic energy of.
But that is just one atom, in the solid we have N
total atoms
this looks more like
Now that is a lot more than my 100 J of kinetic energy of the
object itself.
But this was just the kinetic, the potential in an atom is about
the same amount giving me 120,000 J
This is a lot of energy, but in practicality we never see it.
It just is. It is related to the temperature of the object, but
we won't get to that for a few chapters yet.

for now just realize the definition of thermal energy is
Great so lets talk about thermal energy.

As we have talked about and demonstrated
a text book sliding across the desk gains
thermal energy.

If I pull it at a constant speed, the work of
Tension would equal the change of thermal
energy.
This looks like:

But due to Newtons laws we can say
that the force of Tension = Force of friction
Although this looks like a great result
it doesn't tell us as much as we would like.

It says that the work done by friction equals
the change in thermal energy.
And this is true.
BUT
It doesn't say which objects thermal energy
We can' separate the book from the desk.
Energy model
We previously broken Work into conservative and
non conservative parts
Let us take that one step further and break the
non conservative work into
Dissipative
External
External forces are just that.
For example, pushing a book, or pulling a sled

I ask: are they really non conservative?

Answer: yes, just think about the path I would lift the book
Dissipative forces give rise to dissipative work,
these come from any form of drag, friction, air
resistance, etc.

The only trick here is the system.
We need all of it, for this term, both the book and
the table, both experience friction, and hence
dissipation.
So that makes are work turn into these three
making some substitutions
Work- kinetic energy theorem
Work & conservative forces
Thermal energy and dissipative forces
Here we have the total energy of a system
is equal to the external work being done to it.

If the system is isolated, then the total energy
is conserved. Granted the energy can be transferred
between different parts.
In perhaps a little more user friendly form
From here it is all about before and after shots.
Find what you want to call initial and final, and
go from there.
So this is a good start, but what happens in an oven
The thermal energy goes, up, but there is no velocity
no height, no force....
HEAT
Not until chapter 16-19 or so.
Example 48 I'll do A you do B (modified)
Power
Are we there yet?

The question of How long? is still needing to be answered

Work has been done, but how long did it take.

This is power
Power is the rate of the transfer of energy
The units of power are Watts
We have been playing with Work in this chapter
There have been many types of work, that effect
the energy of the system.
We will just say 'work' here
Looking at the small changes we would say that
a force acting on a particle for a small distance
give a small amount of work:
dividing both sides by a small amount of time
This equation says
If an object is to maintain a velocity while
working against a force, it needs this much power.
Consider a block sliding down a hill
The force here is due to gravity
Substitute, this cosine theta ds = dy
and get

or a final version with out small steps:
Note this work is independent of the path that
it takes to get there.
I could have dropped the block of a cliff of same
height, and gravity would do the same about of
work.
So a force that is bath independent is called
a conservative force.

Now this was just gravity, but any conservative
force that is path independent works

you'll also notice that the Work is equal to a
change in potential energy.

This potential energy came from a conservative
force, Again any conservative force.

Look at a spring.
This brings up the following result
More specifically:
Where Work is made up of both conservative
and Nonconservative parts
From this result and the work kinetic
energy theorem we get
From this we see Mechanical energy is conserved
if there are only conservative forces
Before we leave this analysis let us look at one more thing
This says that the derivative of potential energy with respect
to position is the negative force.
or think of a slope of energy vs position.
"Could you do example 11.9 on page 294 in class?"
"How is it that dissipative forces always increase in thermal energy? Is that just saying it always heats up?"
"What other types of forces are nonconservative other than friction?"
" I can't get how dissipative forces work. Can you explain them?"
"If we could just discuss the last formula for the conservation of energy in the system as a whole with thermal energy involved."
"Will you explain why the slope of a potential energy vs time graph is velocity and not work?"
" Can you please go over example 10.7?
The three ropes are shown in a birds-eye view, dragging a crate 3.0 m across the floor. how much work is done by each of the three forces?
v
F =660 N
F =410 N
F =600 N
3
2
1
30 degrees
20 degrees
A box of mass m and initial speed v_0 slide distance d across a horizontal floor before coming to rest. Use work and energy to find an expression for the coefficient of kinetic friction.
A baggage handler throws a 15 kg suitcase down a ramp of 20 degrees with a constant speed of 1.2 m/s the suitcase slides 2.0 m before stopping. What is the suitcase's coefficient of kinetic friction on the ramp?
An 8.0 kg crate is pulled 5.0 m up a 30 degree incline by a rope angled at 18 degrees above the incline. The tension in the rope is 120 N, and the crate's coefficient of kinetic friction on the incline is 0.25.
How much work is done by tension, by gravity, and by the normal force?

What is the increase in thermal energy of the crate and incline?
v^2/2gd
.364
1691 J
-1980 J
1065 J
-196 J
0 J
571 J
38.5 J
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