The first exam is Thursday. The exam will consist of 10 multiple choice questions, the questions will be variations of the assigned homework problems (i.e. different given values, different wording of the question, etc.). Although the questions are multiple choice, you will need to do some calculations to arrive at an answer. To get credit for a problem, you need to show some work for the problem -- random guessing will not receive credit. The exam will cover chapters 1 to 4. Relevant equations and constants will be printed on the cover sheet.
You will be asked to sit with 2 empty seats between you, and aligned by rows. The exam is closed book and notes. You are allowed to use a calculator.
Dr. Rao invites students from his Thursday quiz section who want some additional review to attend tonight's quiz section. He, Dr. Talagala and I will be available Wednesday and Thursday for questions.
The book has a web site at http://www.saunderscollege.com/physics/college . To login to the student site you will need the username, cpstudent35, and password, phyisfun. WARNING: I looked at the site, went to the chapter 2 quiz problems, and found that the answer to the first problem is wrong. I haven't had time to check other things on the site, but this is not a good sign!
Energy is an extremely important concept in physics, however energy is an abstract idea. You can't simply look at a piece of coal and see it's energy! We begin to understand energy by relating it to mechanical quantities, the first of which is work.
Work has a distinct definition in physics. Work is done on an object when a force is applied to move an object a distance s in the direction of the force, or an object is moved a distance s, with a component of the force F along the motion.
W = (F cost)s
The cost factor takes care of any difference in direction between F and s. The unit of work is the joule (J). From the definition, 1J = (1N)(1m) = 1Nm.
This definition differs considerably from everyday usage of the word "work". If you stand, holding 20kg of books, you will eventually feel more tired, and probably think it is because it's alot of work to hold 20kg of books. But, since the books don't move, no work is done according to the physics definition!!
W = F cost s. The force on the books must be just larger than, and opposite to gravity, so the angle between the force and the motion is 0 degrees. Thus W = Fs = (20kg)(9.8m/s2)(2m)= 392kg m2/s2 = 392J.
Work is done to lift the books, since a force must be applied to overcome the force of gravity on the books, and negative work is done when the books are lowered. Negative work means that we get energy out of the books, but more about this when we discuss energy.
When an object moves with a constant acceleration, then W = Fs = (ma)s. But we also know that v2 = v02 + 2as, or as = ( v2 - v02 )/2. Using this in the expression for work gives:
W = m(v2-v02)/2 = (1/2)mv2 - (1/2)mv02.
We call the quantity (1/2)mv2 the kinetic energy, and write KE = (1/2)mv2. Thus we can say that W = KEf - KEi, or in words, the work done on an object equals the change in its kinetic energy.
A car traveling with speed v skids a distance d when its brakes lock. If the car is traveling with speed 2v, and the brakes apply the same stopping force as before, how far will it skid?
Since W=Fs=DKE, and F remains constant, we see that s = DKE/F. If the speed doubles, then the KE quadruples (and also DKE), so the stopping distance also quadruples. So the car will skid a distance 4d.
The books of the earlier example didn't have KE after they were lifted, yet work was done. Work was done to counteract the force of gravity, and change the position of the books in the Earth's gravitational field. If the force supporting the books is removed, the books will free fall, gaining KE equal to the work done to lift them. Because the books have the potential to do a certain amount of work, we say that they have gained "potential energy" or PE.
If the books were allowed to drop, then the work done by the gravitational force is W = mgs = mgyi - mgyf. We call the quantity mgy the PE, PE=mgy. So the work done by gravity on the books is W = PEi - PEf.
Sketch. a) PE = mgh = (40N)(2.0m) = 80J. b) PE = mgh = (40N)(2.0m)(1-cos(30)) = 11J. c) PE = mgh = 0J.
A force is conservative if the work it does on an object moving between two points is independent of the path the object takes between the points. If the path is closed, so that the final position is the same as the starting postion, then the work done is zero if the force is conservative.
A force is non-conservative if it leads to a dissipation of mechanical energy.
| Force | |
| Gravity | Conservative |
| normal | Conservative (acts perp. to motion) |
| Friction | Non-conservative |
| Spring force | Conservative |
If a particular system involves only conservative forces, then W = PEi-PEf = KEf-KEi, and we can write
KEi+PEi = KEf+PEf = constant
This is a statement of conservation of mechanical energy. Conservation of mechanical energy holds when there is no mechanism for adding additional energy (no unaccounted for external forces) or removing energy from the system (no non-conservative forces).
Initially he has only PE. Make PE=0 at the bottom of the swing, then at
the bottom he has only KE, and his KE at the bottom will equal his PE at 37.0deg.
PE = mgh = mg(30.0m)(1-cos(37)) = 6.04mg.
KE = 1/2 mv2 = PE = 6.04mg
v = [2(6.04)g]1/2 = 10.9m/s