Download chapter02posta

Basic Theme of the Course:
Energy flows through the
Society
• Energy is never destroyed (law of
conservation of energy)
But it changes form.
What are the forms?
Forms of energy we will consider
Kinetic
Gravitational Potential
Thermal
Chemical
Electrical
Electromagnetic (in light)
Nuclear
Thermal
Thermal
Fig. 2-1, p
Our goal is now is to help you understand what these
different forms of energy are and something
about how they are measured so that,
for example, a company can charge you a
definite amount of money for a measured amount
of electrical energy.
Defining energy in physics:
As with everything else in physics, we
start with measurements of length and time,
which we suppose we know how to do.
From our ability to measure length we can
measure the POSITION of an object at each
moment in time. It involves three numbers
at each time (distance forward, sideways,
up/down) .
From position data for each time, we can
get the speed (and if we know the direction,
also the velocity)
For example let’s take some
data from the lab. The times and positions
are both measured from the start of the
motion of a cart.:
(a)Time
(s)
1.00
1.05
1.10
1.15
position
(m)
.390
.410
.429
.448
How would you calculate the speed from
this data?
Definition of speed
Speed= (distance gone)/(time elapsed)
From 1.00 s to 1.05 s, the time elapsed is .05s
The distance gone is .410-.390=.020m
So the average speed in the interval was
.02m/.05s =.4m/s
The instrument which directly measured
speed gave
Time(s) position(m) speed(m/s)
1.00
.390
.388
1.05
.410
.386
Summary:
Average speed= distance gone/time elapsed
Instantaneous speed is defined the same
way but the time elapsed must be extremely
small.
In our calculation above, either the time was
not small enough or the instrument was
not measuring the instantaneous speed
exactly.
Suppose you live 15 miles from the U and you
drove in today in ½ hour. What was your
average speed?
a. 15mph
b. 30mph
c. 7.5mph
d. Can’t tell from this information
Answer b.
15mi/(1/2 hr)=30 mi/hr
Which of the following sets of speedometer
readings could have occurred if you made
the 15 mile trip in ½ hour?
a. 20 minutes at 60mph and 10 minutes at 10mph.
b. 15 minutes at 40mph and 15 minutes at 20mph.
c. 15 minutes at 50mph and 15 minutes at 20mph.
d. None of these.
Answer b:
40mi/hr(1/4hr)+20mi/hr(1/4 hr)=15 mi
The others can be shown not to work.
Velocity is specified by giving speed
AND direction.
30mph is the speed
30mph north specifies velocity
The sign of the velocity
gives the direction if the motion
is in a straight line.
At what points is the velocity zero?
A. 1 only
B. 1 and 3
C. 1,3 and 6
D. 5 and 7
E. 2 and 4
chap 2 Q7
What is the sign of the velocity where it is
not 0?
A. <0 at 1 and 6;>0 elsewhere
B. <0 at 7 ; positive elsewhere
C. <0 at 7; >0 at 2,3,4,5
D.<0 at 2 and 7; >0 at 4 and 5
E. never <0
chap2 Q 8
Acceleration
From the data giving position at each time
we can also get acceleration. It is defined as
Acceleration= (change in velocity)/elapsed time
This is the average acceleration in the elapsed time.
If we make the elapsed time extremely small, we
get instantaneous acceleration. Let’s use the same
data on the car to get the acceleration of the car.
Time(s) position(m) speed(m/s)
1.00
.390
.388
1.05
.410
.386
Here is some of the data on the car which we were
looking at before. Assuming that the speed readings
are right, what was the average acceleration between
1.00 s and 1.05 s?
A. .4m/s2
B. -.4m/s2
C. .04m/s2
D. -.04m/s2
E. None of these
chap 2 Q 3
Answer d:
(.386 m/s-.388m/s)/(1.05 sec-1.00sec)=
(-.002m/s)/(.05s)=-.04m/s2
At what points is the acceleration zero?
A. 1, 5, and 7
B. 1,3,5 and 7
C. 3 and 6.
D. 2 and 4,
E. 1,2 and 4.
chap 2 Q9
What is the sign of the acceleration when it
is not zero?
A. <0 at 7; >0 at 5
B. <0 at 2 and 6; >0 at 3 and 4
C. <0 and 2 and 6;>0 at 4
D. <0 at 2; >0 at 4
E. <0 at 6; >0 at 3.
Chap 2 Q 10
Constant acceleration.
In some kinds of motion, including
free fall of an object in the gravitational
field of the earth, the instantaneous
acceleration of a moving object remains
the same over some time interval.
In that case, the average acceleration is
the same as the instantaneous acceleration,
a plot of speed versus time is a straight line,
and the average speed is ½ the sum of
the initial and the final speed.
Suppose you accelerate your car from
zero speed to 60mph in 1 minute.
Assuming that your acceleration was
constant, what was your average speed and
how far did you go during that one minute?
a. 60mph and 1 mile
b. 30mph and ½ mile
c. 30mph and 1 mile
d. 60mph and ½ mile
e. 30mph and 30miles.
Answer b:
Average speed =60mph/2=30mph
Distance =average speed x time
= 30mph x(1/60 hr)=1/2 mi
Mass
So far, we have described a moving object
by giving its position for each time during its
motion. From the position data we can get the
velocity and the acceleration at each instant.
For a full description, we also need to know the
MASS of the object. We get this by using a
balance to compare the object to objects with
known mass. All such sets of objects of known
mass have been compared through a chain of
measurements with an international standard of
mass. Mass is not exactly the same as weight.
We return to this. We will usually use the kilogram
as a unit of mass. Near the surface of the earth,
a 1 kg object weighs about 2.2 pounds.
Force
Now we can say exactly what we mean by
the total or net force on a moving (or non moving)
object. By definition
The total force on an object =
(Its mass)x(Its acceleration)
This is usually called Newton’s second law
and is written F=ma. However it really is just
a definition of the total or net force on an object
until we say something later about the origin of
forces.
A baseball player slides into third base.
What are the directions of his velocity,
acceleration and the total force on his body ?
velocity
acceleration
total force
A.
toward 3rd toward 3rd
away from 3rd
B.
toward 3rd
away from 3rd toward 3rd
C.
toward 3rd
away from 3rd away from 3rd
D.
away from 3rd toward 3rd
toward 3rd
E.
toward 3rd
toward 3rd
toward 3rd
We now know what the total force on
an object is and we could calculate it if we knew
its mass and the position of the object at each
time in its motion (by calculating the acceleration
from the positions and the time intervals).
However this information would not let us
(or a professional engineer or scientist)
PREDICT what would happen to this object in
the future. For that we need a theory, sometimes
called a model, of what the force is.
Physicists, analysing experiments for over
3 centuries, have found that essentially
all the forces encountered in nature can
be modeled as
Gravitational
Electromagnetic or
Nuclear Forces
Our society uses all of these, but for most
of the course, and in most of everyday life,
we mainly encounter the first two.
Gravitational Force:
This is the force which makes objects fall toward
the earth when you drop them. Even when
studied at a very elementary level (as here)
the gravitational force has properties which make
it act quite differently from forces of the
electromagnetic or nuclear type.
To understand the essential feature, consider
the famous experiment done by Galileo more
than three hundred years ago:
Galilei Galileo lived in Italy from 1564 to 1642
His work on motion preceded Newton’s
theories and provided part of the basis for
them. He lived in Pisa, Italy where, among many
other scientific experiments, he studied the
time for dropped objects made of different masses
and materials to fall to earth. Some of these
experiments were performed by dropping objects
off the leaning tower of Pisa, a famous example
of bad engineering which is still standing (and
was not designed by Galileo).
An essential experimental finding of Galileo’s
experiments is that if only gravity acts on them,
objects of all masses drop toward the surface
of the earth at the same rate, so that if you drop
them from the same height at the same time,
they hit the ground at the same instant.
This had not been understood before and the reason
Galileo got it right (after hundreds of years of
philosophical speculation about it) is that he did
very careful experiments. In fact his first ideas
about how the objects would fall were wrong and
he had to revise them to make them consistent
with his experimental data.
What does this result of Galileo’s
tell us about the gravitational force?
Remember that F=ma or equivalently, a=F/m
so you might think that if the mass were twice
as big, the acceleration would be half as
big. Which of the following resolves this
contradiction with Galileo’s experiments in
a logical way?
A.Newton’s 2nd law does not apply.
B.The acceleration is different but the
time for the drop is not.
C.The gravitational force on an object
doubles if its mass doubles.
D. The gravitational force on an object is
half as big if its mass doubles.
The conclusion is that the gravitational
force on an object is proportional to its
mass.
THIS IS NOT TRUE FOR
FORCES WHICH ARE NOT GRAVITATIONAL