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

Figure 2.1: Illustration of conversions between different forms of energy. Here, solar energy is converted into electrical energy by a solar cell, which is used to run a motor. Fig. 2-1, p. 36

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.: Time position (s) (m) 1.00 .390 1.05 .410 1.10 .429 1.15 .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? 15mph 30mph 7.5mph 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? 20 minutes at 60mph and 10 minutes at 10mph. 15 minutes at 40mph and 15 minutes at 20mph. 15 minutes at 50mph and 15 minutes at 20mph. 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? 60mph and 1 mile 30mph and ½ mile 30mph and 1 mile 60mph and ½ mile 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