READING:

The material covered in today’s class (the continuing topics on work, energy,

conservation of energy, energy conversion, and power) are from Chapter 6, sections 3, 4,

5, 6, 7 in the textbook.

From Chapter #5, from the question section labeled “Conceptual Exercises”

questions #’s: 1, 8, 20, 33, 35From Chapter 5, from the “Review Questions”

Questions # 13, 15, 16 and 17

From Chapter # 6, from the question section labeled “Conceptual Exercises”

questions #’s 8, 15, 21, 27, 36, 37, 39

Last class we considered the effects of gravitational forces on star and planet formation.

We looked at the evolution of the life cycles of stars.

We saw how it depends on the mass of the stars and how it is controlled by gravitational forces.

Stars with masses similar to that of our sun will evolve into white dwarfs.

For stars with masses between 10 and 30 times the mass of our sun, the final stage of evolution is into neutron stars.

Stars more massive than that will evolve into black holes

We distinguished two broad types of energy:

-energy associated with the position of an object (potential energy); and,

-energy associated with the motion of the object (kinetic energy).

Then we moved on to define the work, W, done by a force F in moving an object a distance, d, along the direction of the force as:

W = F·d

We introduced the idea of energy as the capacity to do work.

We saw how work is used to transfer energy.

Definition of ENERGY:

THE CAPACITY TO DO WORK.

When you do work on something, you give it energy in some form.

We call the energy that the block has when it’s not moving and it is above the ground, gravitational potential energy. This is energy the block has because of its position.

And the energy associated with motion is called kinetic energy.

200 kg

In doing work on our block by lifting it, we gave the block gravitational energy (sometimes called gravitational potential energy).

Egrav=mgh

hGravitational potential energy is just the product of weight by the height above the ground.

There is law that summarizes what we have done: the work we did on the block was converted to some type of energy.

The work-energy theorem:

Work is a transfer of energy. Work reduces the energy of the system doing the work and increases the energy of the system on which work is done by an amount equal to the work done.

Work serves to transfer energy from one system to another.

The raised iron block has an ability to do work. It can drive the stake into the ground.

It has potential energy.

What about the dropped block?

Does a moving object have energy?

Consider the following:

mv

m

m

mv=0

h

This observation suggest that all of the motion energy was converted to gravitational potential energy!

ramp

mv

m

m h

Let us know allow the object to go back:

v=0mNow we have manage to convert all

the gravitational potential energy ofthe object into kinetic energy:

ramp

The energy of motion is called kinetic energy (EKIN). What do you think factors in to how much kinetic energy an object has?

Clearly before it started moving it had an amount ofpontential energy that is proportional to its mass:

Epot = mgh

EKIN = ½ mv2

EKIN is related to its velocity and its mass by the following equation:

Thus, the fact that these two forms of energy can interconvert, suggest that the mass also should appear in the expression for kinetic energy.

We also expect that the energy of the moving body would depend on how fast the object is moving, i.e., its velocity.

Does a coiled spring have energy?

Consider the following:

m

m

h

If the spring was able to do work on the ball, the spring had given energy to the ball and it has correspondingly lost energy itself. The energy “stored” in a deformed object is a form of potential energy known as “elastic” energy.

Elastic Energy

Espring = ½ kx2

It makes sense that the stiffer the spring, the biggerthe energy stored in the spring. Also, the larger thecompression, the larger the energy stored.

Espring = ½ kx2

x

Spring strength

Compression distance

Is HEAT energy?

Consider the following:

m

Stove heater

m h

While studying atomic theory we saw that heat was related to the microscopic motion of particles (as the temperature increases, so does the microscopic motion of the atoms or molecules in a gas or liquid, or the vibration of the atoms in a solid).

We will reserve the term “kinetic energy” for motion that is macroscopically observable, i.e. for the motion of an object as a whole.

And we will call “thermal energy” the energy linked to the microscopic motion of particles within a body.

Thermal vs Kinetic Energy

When we heat an object, we “store” this energyinto the vibrations and the motions of molecules in the object.

Thus, we see that heat is a form of energy. It isenergy that can be used to do work and to lift,for example, a body against gravity or to movea piston.

This is the bases of the heat engine.

We call this form of energy thermal energy.

We have described kinetic, elastic (spring) and heat energies in terms of conversion into gravitational energy. What other types of energy are there?

Electrical

Chemical

Nuclear

Radiant (light)

Mass energy (E = mc2 – Einstein)

How could these types of energies do work? For instance, how could we get them to do gravitational work?

Stove coil

m h

Easy: if any of these produce heat, then we can replace our stove coil with a different heat source (say a hot chemical reaction), which will in turn move the piston and convert it into gravitational energy.

The process I have been describing is called an energy conversion: the process by which one type of energy is transformed into another type of energy.

mv

mv=0

hAll Kinetic

All gravitational

Identify the energy conversions in the following processes

[1] Gasoline powered car.

[2] Battery powered laser pointer.

[3] Sun.

[4] The human body. (***)

What do you think is the main single source of all power on the earth?

Now, back to the kinetic energy example:

m

m

hv

What is the gravitational energy at the top? mghWhat is the gravitational energy at the bottom? zeroWhat is the kinetic energy at the top? zeroWhat is the kinetic energy at the bottom? ½ mv2

Is the kinetic energy of the ball before it went up the ramp equal to the kinetic energy when it came back down? YES!

Neglecting friction, the kinetic energy before it wentup is equal to the kinetic energy when it came backdown and it is equal to:

½ mv2

Somehow, the energy of the ball when it went up waspreserved even though at one point (up) it convertedall to gravitational potential energy.

Let’s go back to Galileo and try to see if this is indeedthe case:

The energy at the top of the ramp is Epot = mgh

We want to calculate what is the energy of the ball when it gets at the bottom of the ramp, after falling by a height h.

The ball starts with velocity = 0 at the top. The law of falling bodies says that, the ball will fall a height h ina time t, according to:

h = (1/2)gt2

That means that the ball reaches the ground at time

€

t =2hg

The final velocity of the ball as it reaches the groundis:

€

v f = gt = g2hg= 2gh

And the kinetic energy of the ball at the bottom is:

€

E kin =12

mv 2 f =12

m(2gh) = mgh

The total energy of all the participants in any process remains unchanged throughout that process. That is, energy cannot be created or destroyed.

Energy can be transformed (changed from one form to another), and it can be transferred (moved from one place to another), but the total amount always stays the same.

CONSERVATION OF ENERGY: This result is consistent with experiments that have found that energy is always conserved, although it may change its form.

Note that the TOTAL Energy, the sum of the kinetic and potential energy remains the same throughout.

This is conservation of energy in action.

So, what happens at the end of the motion, once the acrobat hits the bucket?

The kinetic energy will be converted into thermal energy: water molecules and air will move a little faster.

Energy, once one includes thermal energy, is CONSERVED.

More on thermal energy next chapter.

Law of Energy Conservation:

The total energy of all the participants in any process remains unchanged throughout that process.

Energy cannot be created nor destroyed.

Energy can be transformed from one form to another.

Energy can be moved from one place to another.

But the total amount of energy stays the same.

What is the work done in climbing a flight of stairs of height h?

h

Do you get more tired when you run or when you walk up the stairs?

W=Fd=(mg)h

What is the difference?

DEFINITION of POWER

Power is equal work done divided the time it takes to do it. That is, the rate at which work is done:

What is the UNIT of power?

Power = Work / time

= Joules / seconds

= J / s

= Watt (W)

(Power = Work / time)

h

Example:

What is the power output of a 100 kg person who runs up a 10 m high flight of stairs in 3 s?

[1] W = Fd= mgh= (100 kg)(9.8 m/s2)(10 m)= 9,800 J

[2] P = Work / time= (9,800 J) / (3 s)

=3,266 W

Problem: You have to move 100 bricks onto a ledge that is 1 meter high. Suppose you lift one at a time where it takes 2 seconds to move each brick. If each brick has a mass of 2 kg, how much work have you done when the job was done? What is your power output?

1 m

W = Fd= (Weight) (h)= (mg)(h)=(2 kg)(9.8 m/s2)(1 m)

=19.6 J (per brick!)

Work for the total job:(Work per brick)(# of Bricks)Wtot = (19.6 J)(100)Wtot = 1,960 J

Problem: You have to move 100 bricks onto a ledge that is 1 meter high. Suppose you lift one at a time where it takes 2 seconds to move each brick. If each brick has a mass of 2 kg, how much work have you done when the job was done? What is your power output?

1 m

Wtot = 1,960 JTo get the power we need the total time for doing this workt = (time per brick)(# of bricks)

= (2 s)(100)= 200s

In-Class Problem: You have to move 100 bricks onto a ledge that is 1 meter high. Suppose you lift one at a time where it takes 2 seconds to move each brick. If each brick has a mass of 2 kg, how much work have you done when the job was done? What is your power output?

1 m

Wtot = 1,960 J t = 200s

P = work / time= (1,960 J) / (200 s)= 9.8 J/s= 9.8 W

Problem: Suppose you lift them all at once with a fork lift and the process takes 5 s. What is the work done and what is the power in this case?

1 m

Work must be the same!!Wtot = 1,960 J

P = (work) / (time)= (1,960 J) / (5 s)= 392 J/s = 392 W

= 3.6 x 106 J/s · s

The kilowatt hour

What physical quantity is the kW · h a unit of ?

1 kW = 1,000 W

1 h = 3,600 s

(1 kW) x (1 h) = (1,000 W) x (3,600 s)= (1 x 103 J/s)(3.6 x 103 s)

= 3.6 x 106 J1 kW · h

One horsepower = 750 W. (i.e., a unit of power)

What is the minimum number of horsepower required for a car engine that is supposed to haul a 4,400 lb (2000 kg) car (plus trailer) up a 10,000 foot mountain (3,350 m) mountain in 10 minutes?

P = W/t (so find W first)W = Fd = (mg)(h)

= (2000 kg)(9.8 m/s2)(3,350 m)=6.6 x 107 JW

t = (10 min)(60 s/min)= 600 st

P = W / t= (6.6 x 107 J) / (600 s)= 1.1 x 105 WP

HP= P (Watts)/ 750= (1.1 x 105 W) / (750)

= 146.7 Horsepower