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. 36

Our goal is now is to help you understand what thesedifferent forms of energy are and somethingabout 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 eachmoment in time. It involves three numbersat each time (distance forward, sideways,up/down) .

From position data for each time, we canget the speed (and if we know the direction,also the velocity)

For example let’s take some data from the lab. The times and positionsare both measured from the start of themotion of a cart.:

(a)Time position(s) (m) 1.00 .390 1.05 .410 1.10 .429 1.15 .448

How would you calculate the speed fromthis 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 gaveTime(s) position(m) speed(m/s)1.00 .390 .3881.05 .410 .386

Summary:

Average speed= distance gone/time elapsed

Instantaneous speed is defined the sameway but the time elapsed must be extremely small.

In our calculation above, either the time wasnot small enough or the instrument wasnot measuring the instantaneous speedexactly.

Suppose you live 15 miles from the U and youdrove in today in ½ hour. What was your average speed?

a. 15mphb. 30mphc. 7.5mphd. Can’t tell from this information

Answer b.

15mi/(1/2 hr)=30 mi/hr

Which of the following sets of speedometerreadings could have occurred if you madethe 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 speedAND direction.

30mph is the speed

30mph north specifies velocity

The sign of the velocitygives the direction if the motionis in a straight line.

At what points is the velocity zero?

A. 1 onlyB. 1 and 3C. 1,3 and 6D. 5 and 7E. 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 elsewhereB. <0 at 7 ; positive elsewhereC. <0 at 7; >0 at 2,3,4,5D.<0 at 2 and 7; >0 at 4 and 5E. never <0

chap2 Q 8

Acceleration

From the data giving position at each timewe 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 samedata on the car to get the acceleration of the car.

Time(s) position(m) speed(m/s)1.00 .390 .3881.05 .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 between1.00 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 7B. 1,3,5 and 7C. 3 and 6.D. 2 and 4,E. 1,2 and 4.

chap 2 Q9

What is the sign of the acceleration when itis not zero?A. <0 at 7; >0 at 5B. <0 at 2 and 6; >0 at 3 and 4C. <0 and 2 and 6;>0 at 4D. <0 at 2; >0 at 4E. <0 at 6; >0 at 3.

Chap 2 Q 10

Constant acceleration.

In some kinds of motion, includingfree fall of an object in the gravitationalfield of the earth, the instantaneousacceleration of a moving object remains the same over some time interval.

In that case, the average acceleration isthe same as the instantaneous acceleration, a plot of speed versus time is a straight line,and the average speed is ½ the sum ofthe 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 mileb. 30mph and ½ milec. 30mph and 1 miled. 60mph and ½ milee. 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 objectby giving its position for each time during itsmotion. From the position data we can get thevelocity and the acceleration at each instant.

For a full description, we also need to know theMASS of the object. We get this by using abalance to compare the object to objects withknown mass. All such sets of objects of known mass have been compared through a chain ofmeasurements with an international standard of mass. Mass is not exactly the same as weight.We return to this. We will usually use the kilogramas 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 bythe 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 justa 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 forceA. toward 3rd toward 3rd away from 3rdB. 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 onan object is and we could calculate it if we knewits mass and the position of the object at each time in its motion (by calculating the accelerationfrom 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, sometimescalled a model, of what the force is.

Physicists, analysing experiments for over 3 centuries, have found that essentiallyall the forces encountered in nature canbe 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 towardthe earth when you drop them. Even when studied at a very elementary level (as here)the gravitational force has properties which makeit act quite differently from forces of the electromagnetic or nuclear type.

To understand the essential feature, considerthe famous experiment done by Galileo more than three hundred years ago:

Galilei Galileo lived in Italy from 1564 to 1642His work on motion preceded Newton’stheories and provided part of the basis forthem. He lived in Pisa, Italy where, among manyother scientific experiments, he studied thetime for dropped objects made of different massesand materials to fall to earth. Some of theseexperiments were performed by dropping objectsoff the leaning tower of Pisa, a famous exampleof bad engineering which is still standing (andwas not designed by Galileo).

An essential experimental finding of Galileo’sexperiments is that if only gravity acts on them,objects of all masses drop toward the surfaceof 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 reasonGalileo got it right (after hundreds of years of philosophical speculation about it) is that he didvery careful experiments. In fact his first ideasabout how the objects would fall were wrong andhe had to revise them to make them consistentwith his experimental data.

What does this result of Galileo’stell us about the gravitational force?Remember that F=ma or equivalently, a=F/mso you might think that if the mass were twiceas big, the acceleration would be half asbig. Which of the following resolves this contradiction with Galileo’s experiments ina logical way?A.Newton’s 2nd law does not apply.B.The acceleration is different but thetime for the drop is not. C.The gravitational force on an objectdoubles if its mass doubles. D. The gravitational force on an object ishalf as big if its mass doubles.

The conclusion is that the gravitationalforce on an object is proportional to itsmass.

THIS IS NOT TRUE FORFORCES WHICH ARE NOT GRAVITATIONAL