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Physics 1102
Introductory College Physics II
Lectures: 5:45pm-7:25pm in Willey Hall 125
(there will be a 10minute break from 6:30-6:40pm)
Instructor: J. Woods Halley (email: [email protected])
Course web page:
http://www.physics.umn.edu/courses/2017/spring
A few administrative clarifications:
Permissions: If there are openings
in a lab session to which you want
to switch, go to the session and ask
the TA if there is room. If there is,
give him your name and he will contact
me to help arrange the switch.
Registration in the whole
course is limited to 19 people per lab section
because of available lab space.
If registration drops below that level
then new registrants can register on
line. No permission numbers will be
given for registration over the limit.
Background from Introductory Physics I (1101)
Newton's laws of motion and how to use them.
What we will do in 1102:
Properties of Solids and Liquids:
Often Newton's laws apply, but new features
arise when we consider the behavior of the
atoms in these many atom systems leading
to thermal physics and laws of thermodynamics
Electricity and Magnetism: Providing new forces
in Newtonian equations.
Structure of Atoms: Newton doesn't work on
very small scales.
Conservation of energy and forms of energy:
Let's consider a dropped ball.
As I release it, its velocity is zero.
As it gets to the floor, it's attained a finite velocity v.
From what we know already, we can figure out
the relationship between the height h from which
it was dropped and the speed v, which it had when
it hit the floor:
distance fallen h = average speed x
time=(1/2)vxtime
(F=ma for a dropped ball.)
v=time x g
Therefore time =v/g. Put it in the 1st equation:
h=(1/2)v(v/g) or gh=(1/2)v2
Kinetic and gravitational potential energy.
From F=ma and the fact that the gravitational
force is mg, we thus conclude that, for the dropped ball:
gh=(1/2)v2
or multiplying both sides by m
mgh=(1/2)mv2
at start just before it hits
We say that the ball had
Gravitational potential energy =mgh
At the start of its fall and that energy changed
form and became
Kinetic energy = (1/2)mv2
Just before the ball hit the floor
Thus for one isolated body,
kinetic energy =1/2 mv2 +
(gravitational) potential energy =mgh
is conserved through free fall in the
earth's gravitational field.
Generalization:
Kinetic plus potential energy
for an isolated collection of
interacting particles is conserved
(as in a gas or liquid)
.
Potential Energy:
Generally, a system which can evolve according
to Newton's laws to have more kinetic energy
is said to have initially had a form of
potential energy.
Examples: gravitational mgh
elastic in springs ½ kx2
chemical
I will show that elastic energy + kinetic energy
is conserved for a mass m on a fixed spring
with constant k:
Consider two moments 1 and 2, close together
in time, during the motion.
F =-kx =ma=m(v2-v1)/(t2-t1)
multiply by v≈(v2+v1)/2 and by t2-t1
write x≈(x2+x1)/2
and (t2-t1)v =x2-x1
Rearranging, you will find
½ mv12 +1/2 kx12 = ½ mv22 +1/2 kx22
Chemical Energy
The forces between atoms don't always act like
springs. But those forces do store potential energy
which can be converted to kinetic energy.
You may think of chemical energy as the potential
energy stored in the bonds between the atoms
of a system.
Thermal Energy
This is the part of the kinetic plus potential energy
of a system of many atoms which does not arise
from coherent motion of all the atoms.
Picture a baseball in flight and a balloon on
a string (not in flight). The atoms in the baseball
are all moving in the same direction (coherent).
The atoms in the balloon are all moving in different
directions (incoherent).
Δ contains
coherent
K
parts of the
velocities, as in the
thrown baseball.
ΔEth contains kinetic
energy of the
incoherent parts of
the velocities, as in
the air in the hot
balloon.
Summary for isolated systems:
The change in the total energy
ΔE = ΔK +
ΔU+
ΔEth +
ΔEchem =0
kinetic potential thermal chemical
Example: A bomb lying motionless on
the ground explodes.
A person lifts her arm.
There are many more but, often, systems aren't
isolated.
Energy Transfer between systems:
One way is by the performance of work:
example: lift a book
throw a baseball
games with carts
The transfer of energy can be to or from any
of the four forms we have mentioned.
Energy Transfer between systems:
One way is by the performance of work:
example: lift a book
throw a baseball
games with carts
The transfer of energy can be to or from any
of the four forms we have mentioned.
If work is performed on (or by) a system
from the outside world then the previous
relation becomes
ΔE = ΔK +
ΔU+
ΔEth +
ΔEchem =W
where W is the work done ON the system.
In many applications of the conservation
of energy, the system at hand
(an engine, your body) does work on the
external world (then W <0) . Consider
lifting a book:
The work done by my body on the book
is mgh.
It came from the chemical energy in
my body.
The work done by my body on the book
is mgh.
It came from the chemical energy in
my body.
Is it true that
ΔEchem =W=-mgh for this process?
a. yes, it's required by conservation of
energy
ΔEchem
=W=+mgh
b. no, because my arm
warms
up
c.
should
be by the second law of
d. no,
yes,itit's
required
thermodynamics.
The answer is b. Some of the chemical
energy is converted to thermal energy.
The second law of thermodynamics says
that such processes never succeed in
converting all the input energy into
coherent motion associated with work.
Thus the energy balance equation for
lifting the book takes the form
ΔEth +
ΔEchem =-mgh
with ΔEchem <0 and ΔEth>0
Efficiency:
The efficiency for this booklifting exercise is
defined as
e = -W/ (-ΔEchem)
The signs can be confusing:
W is the work done ON the system (my
body) so W<0 when I lift the book.
The chemical energy in my body was
depleted so ΔEchem <0
So e >0 and e will always be between 0 and 1
by the 2nd law of thermodynamics.
Metabolism:
Metabolism is the rate at which chemical energy
is converted to coherent work (done by your
muscles) and thermal energy in your body.
Energy is stored in your body in the form of
glucose which has the composition
C6H12O6 meaning that the molecule consists of
six carbon atoms, 12 hydrogen atoms and 6 oxygen
atoms, bound together. In the process by
which the chemical energy is released this molecule
interacts with oxygen in your blood (which you
got by breathing) as follows:
C6H12O6 + O2
6CO2 +6H2O + energy
Metabolism:
Metabolism is the rate at which chemical energy
is converted to coherent work (done by your
muscles) and thermal energy in your body.
Energy is stored in your body in the form of
glucose which has the composition
C6H12O6 meaning that the molecule consists of
six carbon atoms, 12 hydrogen atoms and 6 oxygen
atoms, bound together. In the process by
which the chemical energy is released this molecule
interacts with oxygen in your blood (which you
got by breathing) as follows:
C6H12O6 + O2
6CO2 +6H2O + energy
Structure of glucose. Black is carbon atom,
red is oxygen atom, blue hydrogen.
Size is about 1 billionth of a meter.
More generally, efficiency is
e = work (energy associated with coherent motion) out
thermal and chemical energy into system
We usually consider what happens in 'steady state'
when determining efficiencies. Then total outflow of
energy per second equals total inflow (First law of
thermodynamics). In the case of lifting a book,
in steady state, the depletion of chemical energy
will be replaced (when I eat and digest food) so -ΔEchem
is the energy input.
Generic diagram of energy flow in devices
which output work from atomically incoherent
sources (thermal energy and chemical energy)
--
if system is red box
(the 'engine') then using
the definition of W in the
work energy theorem, the
work output is -W.
Thermal engines.
The energy input is all thermal, usually at a
high temperature Th . The thermal energy
output Qc is at a lower temperature Tc .
The second law of thermodynamics say
the we must have Qc >0 and e < 1.
It is best to think of the diagram as representing
energy flows in steady state and to replace Qc by
Qc /t , Qc by Qc /t , and -W by power output P.
An example is a car. Thermal energy is produced
when the carbon in the gasoline is combined
with the oxygen of the air via the reaction
(combustion or burning)
C + O2
CO2 + thermal energy
to provide thermal energy input to the engine.
The output work is used to push the car forward.
If the fuel efficiency of your car is 35 miles per
gallon how much energy is being provided to
your engine for each mile you drive. (1.32 x 108 joules of
thermal energy are available per gallon of gasoline.)
A. 1.32 x 108 joules
B. 3.77 x 106 joules
C. 4.62 x 109 joules
D. 2.03 x 106 joules
If the fuel efficiency of your car is 35 miles per
gallon how much energy is being provided to
your engine for each mile you drive. (1.32 x 108 joules of
thermal energy are available per gallon of gasoline.)
A. 1.32 x 108 joules
B. 3.77 x 106 joules
C. 4.62 x 109 joules
D. 2.03 x 106 joules
Answer B.
If the thermal efficiency of your car is
30% how much energy is being used
to push the car forward per mile
(if the gasoline is providing 3.77 x 106 joules of
thermal energy per mile)
A. 1.13 x 106 joules
B. 2.64 x 106 joules
C. 7.54 x 104 joules
D. 3.96 x 107 joules
Answer A.
.30x 3.77 x 106 joules/mi=
1.13 x 106 joules/mi
What force is the engine providing to
drive the car forward in the last example
(in Newtons). The energy provided in
a mile was 1.13 x 106 joules (1 mile=1600 meters)
A. 212 Newtons
B. 1.81 x 109 Newtons
C. 5.43 x 108Newtons
D. 706 Newtons
Answer D.
Work = F x 1mile =1.13 x 106 joules
F=1.13 x 106 joules/1600 meters = 706 Newtons
What power, in horse power is the engine
producing at 35mph in this car? (The
force was 706 Newtons).
1 pound(lb)=4.4 newtons,
1 mile = 5280ft, 1 horsepower=550ft-lb/s
A. 291 hp
B. 15 hp
C. 7 hp
D. 0.4 hp
Answer: C
(706 Newtons x 35mph x 5280 ft/mi)
/(3600 sec/hr x 4.4 N/lb x550 ft-lb/hp)=15hp
A takehome message is that cars
are overpowered.
Now let's consider a bigger 'engine': the
US energy economy.
Look over at the right:
The gray box says 'Rejected energy'. That's
energy that wasn't used usefully by humans.
The black box says 'Energy services'. That's
energy that was useful for humans.
Estimate the efficiency of the US
energy economy.
54.64
A. 42%
B. 73%
C. 58%
D. 136%
39.97
A
This is somewhat misleading because a
significant portion of the energy which was
used was thermal energy (for heating
buildings.)
So far we briefly discussed these processes that
change the form of energy:
gravitational potential energy to KE (falling object,
also hydropower)
chemical energy to atomically coherent KE and PE
plus thermal energy (humans)
thermal energy to atomically coherent KE and PE
plus thermal energy (engines)
All these processes involve the performance of work.
There is another way to transfer energy from one
body to another without the performance
of (atomically coherent) work.:
Another way to transfer thermal energy
to a body (not involving the performance of
work)
Transfer of thermal energy from another
body at higher temperature.
This is what happens
in your house or apartment in the winter.
Thermal energy is continuously transferred
to the colder outside air through the walls
and windows.
Similarly from your body to the outside
air when you go out.
And many others...
To analyse thermal energy transfers, we need
a way to measure changes in thermal energy
in a body. Here is a way to do it:
Do an experiment in which work is done on
the body by a force which is entirely frictional
(no acceleration), while measuring the temperature
of the body with a thermometer. The frictional
force excites the atoms in the body and increases
its thermal energy and the temperature rises.
For small changes in temperature, the following
relation holds as long as the body is not at its
boiling or freezing temperature:
work done = thermal energy added =
constant x (change in temperature)
work done = thermal energy added =
constant x (change in temperature)
Experimentally one finds that the constant
depends on the material of which the body
is made.
is proportional to the mass of the body.
Thus the quantity
c = constant/mass
is characteristic of the material of which the
body is made. c is called the specific heat of the material
That process tells you how to measure
the specific heat (measure the work done,
the mass and the change in temperature) and
people have done it and tabulated the
values of specific heats for many materials.
Summary:
The change Q in the thermal energy
of a body with specific heat c and mass
M undergoing a change ΔT is
Q = McΔT
Let's apply this to some situations in which
thermal energy is transferred from one
body (the initially higher temperature one)
to another body (the initially lower temperature one)
A can containing 500gm of water at 100 o C is
put in contact with another can containing
1000 gm of water at 30 o C and the two touching
cans are wrapped in insulation so that no
thermal energy can escape. What is the final
temperature of the water in the cans?
(Ignore any thermal effects of the cans themselves)
specific heat of water =4190 J/kgoC
A. 86.7 C
B. 76.7 C
C. 53.3 C
D. 65 C
Answer C.
The energy lost by the hot water is gained
by the cold water (energy conservation).
.5kgxCwater(100-T)= 1.0kgCwater(T-30)
Solving for T:
(1.5)T=0.5x100+30
T=80/1.5 C=53.3 C
Note: In this case, the specific heat cancelled
out, so it wasn't needed.
The first problem in homework 1 is similar to
this.
Phase Changes
The transfer of thermal energy from
one body to another proceeds differently
if the body is undergoing a PHASE CHANGE.
Phase changes can be recognised experimentally
by the occurrence of abrupt changes in
properties. The most common examples are
Melting (solid to or from liquid)
Boiling (liquid to or from vapor)
The thermal energy absorbed or released
during a phase change is characterised by
the HEAT OF TRANSFORMATION L of
the material.
ΔQ = ±ML
where M is the amount of mass which has
undergone the phase change and the sign
is
+ if going from the low temperature phase
to the high temperature phase (eg melting)
- If going from the high temperature to
the low temperature phase (eg freezing)