EXAM II, PHYSICS 1403 1. 2. 3. 4. November 2, 2004 Dr. Charles W. Myles INSTRUCTIONS: Please read ALL of these before doing anything else!!! 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! PLEASE show all work, writing the essential steps in the problem solution. 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. The setup (PHYSICS) of a problem will count more heavily than the math of working it out. 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 125 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!! A 8.5’’ x 11’’ sheet with anything on it & a calculator are allowed. Problem 1 (Conceptual Questions) IS REQUIRED! Answer any two (2) of the remaining problems for a total of three (3) problems required. Problem 1 is worth 34 points. Problems 2, 3, and 4 are equally weighted & worth 33 points each. 1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer briefly, in a few complete and grammatically correct English sentences. Supplement these sentences with equations, but keep these to a minimum!! a. State the Principle of Conservation of Mechanical Energy. b. State the Law of Conservation of Momentum. c. See figure. A ball, mass m, is twirled at the end of a string in a vertical circle of radius r and constant speed v. Free body diagrams for the ball at the top and at the bottom of the circle are shown. Is the tension FTA that the string exerts on the ball at the top of the circle (point A) less than, more than, or equal to the tension FTB at the bottom of the circle (point B)? Explain your answer using Newton’s 2nd Law with centripetal acceleration. d. See figure. Two water slides are shaped differently, but they start at the SAME height, h. Two riders, Paul and Kathleen, start from rest at the same time and at the SAME height h but on different slides. (The figure shows them at different heights because it shows them AFTER they have started down!) The slides are frictionless. Which rider is traveling faster at the bottom? What physical principle did you use to answer this? Which rider gets to the bottom first? Why ? (Answer in words!!) e. Answer the following for 5 BONUS POINTS! During our energy conservation discussion, I did a demonstration which illustrates the answer to part d about the people on the water slides. Briefly describe this demonstration. (If you were in class the day I did this demonstration, you probably will be able to answer this. However, if you “cut” class that day, as many of you often do, you probably won’t be able to answer it!) NOTE: Answer any two (2) of problems 2, 3, & 4!!! 2. See figure. A Ferris wheel moves in a vertical circle of radius r = 10 m at a constant speed v = 5 m/s. A rider of mass m = 50 kg is sitting in one of the cars. This person experiences a normal force FN due to the car seat pushing upward on their body. The free body diagrams for the rider at the top and at the bottom are shown in the figure. The normal force is labeled FN at both the top and the bottom. However, this does NOT imply that FN necessarily has the same numerical value at the two places (it might or it might not)! Part of this problem is to compute FN at the two places! a. Compute the period of the circular motion of the Ferris wheel. b. Compute the centripetal acceleration experienced by the rider. c. Compute the centripetal force on the rider. d. Use Newton’s 2nd Law with centripetal acceleration to compute the normal force FN between the rider and the car seat at the top of the ride. e. Use Newton’s 2nd Law with centripetal acceleration to compute the normal force FN between the rider and the car seat at the bottom of the ride. 3. See figure. A mass m = 4.0 kg slides with initial velocity v = 3 m/s across a horizontal, frictionless surface until it encounters a spring with constant k = 250 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 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 force (magnitude and direction) the spring exerts on the mass at the final position (right hand figure) where the mass has stopped moving. d. 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 1 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!) e. 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? NOTE: Answer any two (2) of problems 2, 3, & 4!!! m 4. See figure. A bullet, mass m = 0.035 kg, traveling at a speed v = 350 m/s, strikes and becomes embedded in a block of wood, M mass M = 1.5 kg, which is at initially at rest on a horizontal v = 350 m/s surface. The block-bullet combination then to moves to the right across the surface. a. Compute the momentum and kinetic energy of the bullet before it hits the block. b. Compute the momentum of the bullet-block combination as they move away from the collision. Compute their speed V immediately after the collision. What physical principle did you use to find these? c. Compute the kinetic energy of the bullet-block combination immediately after the collision. Was kinetic energy conserved? Explain (using brief, complete, grammatically correct English sentences!). (Hint: Please THINK before answering this! Compare the kinetic energy computed here with that computed in part a!) d. Compute the impulse Δp delivered to the block by the bullet. If the collision time was Δt = 2 10-3 s, compute the average force exerted by the bullet on the block. What physical principle did you use to find this force? e. After the collision, the bullet-block combination moves across the horizontal surface until it stops some distance away from the collision point. Assuming that work done by the frictional force between the block and the surface is what causes them to stop, how much work is done by friction in this process? (Hint: I’m not asking for the frictional force here! I’m asking for the WORK [energy!] associated with friction! To answer this, you DON’T need to know the frictional force or the distance it takes to stop!) V=?