**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