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EXAM III, PHYSICS 1403 July 27, 2006 Dr. Charles W. Myles INSTRUCTIONS: Please read ALL of these before doing anything else!!! 1. PLEASE put your name on every sheet of paper you use and write on one side of the paper only!! PLEASE DO NOT write on the exam sheets, there will not be room! Yes, this wastes paper, but it makes my grading easier! 2. PLEASE show all work, writing the essential steps in the solutions. Write appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that essential work is shown. Organized, logical, easy to follow work will receive more credit than disorganized work. 3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out. 4. PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages and put the pages in numerical order, b) put the problem solutions in numerical order, and c) clearly mark your final answers. If I can’t read or find your answer, you can't expect me to give it the credit it deserves. NOTE: I HAVE 85 EXAMS TO GRADE!!! PLEASE HELP ME GRADE THEM EFFICIENTLY BY FOLLOWING THE ABOVE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!! An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed. NOTE: Problem 1 consists of Conceptual Questions and IS REQUIRED! You may work any three (3) of the remaining four problems for four (4) problems total for this exam. Each problem is equally weighted and worth 25 points, for a total of 100 points on this exam. 1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer briefly, in complete, grammatically correct English sentences. Supplement your answers with equations, but keep these to a minimum. Explain what the symbols mean!! PLEASE!! Read carefully & answer ALL questions! a. State the Work-Energy Principle. b. State the Principle of Conservation of Mechanical Energy. c. State the Law of Conservation of Momentum. d. See figure. Paul & Kathleen start from rest (on the left) on two different shaped, frictionless water slides which end (on the right) at the same vertical level. Their starting heights are unknown. However, measurement shows that they have the SAME velocity, v when they arrive at the bottom. Which rider started from the highest point? What Physical Principle did you use to answer this? If they start at the same time, which rider gets to the bottom first? Why ? (Answer in words!!) e. For 5 BONUS POINTS(!!), answer the following: During our class discussion about mechanical energy conservation, I did a demonstration to try to illustrate the answer to part d. Briefly describe this demonstration. (If you were in class the day I did this demonstration, likely will be able to answer this. If you “cut” class that day, as several of you are now habitually doing, you probably won’t be able to answer it!) both have velocity v here NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!! NOTE: Some of answers to the following problems are large numbers! PLEASE express such answers in SCIENTIFIC (power of 10) NOTATION! Thanks! 2. See figures. In a pool game, two balls undergo an elastic collision as they approach each other head-on. Fig. a shows a them before the collision and Fig. b shows them after the collision. The masses are m1 = 0.5 kg & m2 = 0.35 kg. The initial velocity of m1 is v1 = 4.5 m/s & that of m2 is v2 = -3.5 b m/s. The velocities are in the opposite direction as in Fig. a. After the collision, their velocities v1´ & v2´ again in opposite directions, as in Fig. b. a. Compute the total momentum p1 + p2 of the two balls before the collision. (Hint: Don’t forget that momentum is a vector & DIRECTION matters!). Compute the total kinetic energy KE1 + KE2 of the two balls before the collision. b. Compute the total momentum p1´+ p2´ of the two balls after the collision. Compute the total kinetic energy KE1´ + KE2´of the two balls after the collision. What physical principles did you use to find these results? Is kinetic energy conserved in this collision? c. Calculate the velocities v1´ & v2´ of the balls after the collision. d. Compute the impulse that was delivered to m2 by m1. (Stated another way, compute the change in momentum Δp2 of m2 due to the collision.) e. If the collision time was Δt = 7 10-3 s, use the results of part d to compute the average force exerted by m1 on m2. 3. See figure. A mass m = 5.0 kg slides with initial velocity v = 3.5 m/s across a horizontal, frictionless surface until it encounters a spring with constant k = 265 N/m. It comes to rest after compressing the spring a distance x. (Hint: In the following, PLEASE remember to take square roots properly!) Initially, v = 3.5 m/s Finally, x = ?, v = 0 a. Compute the initial kinetic energy of the mass (left hand figure). b. Compute the potential energy of the spring-mass system at the final position and the distance x the spring is compressed there (right hand figure). What physical principle did you use to find these results? c. Compute the potential energy of the spring-mass system and the distance the spring has been compressed when the mass’s speed has slowed down to 2.0 m/s. (This is not shown in the figures! This occurs sometime after the mass touches the spring, but before it has come to rest in as in the right hand figure!) d. The mass in the left hand figure was given its initial velocity by sliding it from rest down a frictionless inclined plane from a height h. (This is not shown in the figures! This happened sometime before the situation shown in the left hand figure!) Compute the potential energy the mass had at the top of the inclined plane and the height h from which the mass started. What physical principle did you use to find these results? e. 5 POINT BONUS!! Compute the FORCE (magnitude and direction) the spring exerts on the mass at the final position (right hand figure) where the mass has stopped moving. NOTE: WORK ANY THREE (3) OF PROBLEMS 2., 3., 4., or 5.!!!!! NOTE: Some of answers to the following problems are large numbers! PLEASE express such answers in scientific (powers of 10) notation! Thanks! 4. See figure. A roller coaster car, mass m = 3,750 kg, is shown a portion of a roller coaster ride. The height difference between points A and B is 55 m. The height difference between points B and C is 42 m. The car starts from rest at point A. Take the y = 0 point to be point B. For parts a., b., and c., assume that the roller coaster track is frictionless. a. Compute the gravitational potential energy of the car points A, B, and C. b. Compute the kinetic energy of the car at point B. What physical principle did you use? c. Compute the speed of the car at point B. d. Compute the kinetic energy and speed of the car at point C. e. Parts a., b., and c. assume that the track is frictionless. However, the measured speed of the car at point B is found to be vB = 25 m/s. This is less than the speed that you (should have) computed in part b. This means that friction can’t be neglected. In this case, how much WORK is done by friction when the car moves from point A to point B? (Hint: I’m asking for WORK here, not for the frictional force! You don’t need to compute the frictional force to answer this!) 5. See figure. A railroad engine, mass M = 55,000 kg, traveling at a speed v = 28 m/s strikes a car, mass m = 5,500 kg, which is at initially at rest because it is stuck in the crossing (the people in the car have run away from it!). After the collision, the railroad engine and the car STICK TOGETHER (it is a perfectly Inelastic Collision!) and move off down the tracks. v = 28 m/s Before Collision V=? After Collision a. Compute the initial momentum and the initial kinetic energy of the engine. b. Compute the momentum of the engine-car combination as they move away from the collision. What physical principle did you use to find this? c. Compute their speed V immediately after the collision. d. Compute the kinetic energy of the engine-car combination immediately after the collision. Was kinetic energy conserved? Was momentum conserved? Explain (using brief, complete, grammatically correct English sentences!) your answers to these questions. e. Compute the impulse Δpcar delivered to the car by the engine. If the collision time was Δt = 8 x 10-3 s, compute the average force exerted by the engine on the car. What physical principle did you use?