Name____________________________________________________ University of Maryland Department of Physics Physics 122 Dr. E. F. Redish Spring 2011 Exam 1 4. March. 2011 *** Good Luck *** Instructions: Do not open this examination until the proctor tells you to begin. 1. When the proctor tells you to begin, write your full name at the top of every page. This is essential since this exam booklet will be separated for grading. 2. Do your work for each problem on the page for that problem. You might find it convenient to either do your scratch work on the back of the page before starting to write out your answer or to continue your answer on the back. If part of your answer is on the back, be sure to check the box on the bottom of the page so the grader knows to look on the back! 3. On all the problems except the multiple choice questions in problem 1 or where it says not to explain, your answers will be evaluated at least in part on how you got them. More than half the credit of the problem may be given for the explanation. YOU MAY EARN LITTLE OR NO CREDIT FOR YOUR ANSWERS IF YOU DO NOT SHOW HOW YOU GOT THEM. Partial credit will be granted for correct steps shown, even if the final answer is wrong. Explanations don’t need to be long, but they need to show what physics you are using and assumptions you are making. 4. Write clearly and logically so we can understand what you are doing and can give you as much partial credit as you deserve. We cannot give credit for what you are thinking — only for what you show on your paper. 5. If you try one approach and then decide on another, cross out the one you have decided is wrong. If your paper contains both correct and incorrect approaches the grader will not choose between the two. You will not receive any credit when contradictory statements are present, even if one is correct. 6. All calculations should be done to the appropriate number of significant figures. 7. At the end of the exam, write and sign the honor pledge in the space below (“I pledge on my honor that I have not given or received any unauthorized assistance on this exam.”): #1: #2: #3: #4: #5: TotalNAME___________________________________________ POINTS_______ Physics 122 Dr. E. F. Redish Spring 2011 Exam 1 If you need more space, continue on the back and check here. 1. (25 points) A sonic ranger is attached to a spring, which is attached to a wheeled cart. The x-coordinate reported by the ranger is shown above the diagram. The small black circle on the axis indicates the point at which the cart’s arrow points when the spring is at its rest length. The cart has been pulled out to a positive x value greater than the rest length and released. After a few oscillations the ranger starts to collect data. At the time at which that happens is taken the cart looks as shown in the picture above and we take it as t = 0. For the time interval shown, friction can be ignored. In the figures below are shown graphs for a number of different variables either taken directly from the ranger’s data or calculated from it. All the graphs are shown as functions of time (horizontal axis). Identify which of the graphs could possibly be graphs of the indicated variables if the vertical axis had the right units. Note that the horizontal axis (with arrow) goes through the zero of the vertical axis in each case. Put all the answers that could be right. If none work, put N. _____ x position _____ x velocity _____ potential energy _____ kinetic energy _____ total mechanical energyNAME___________________________________________ POINTS_______ Physics 122 Dr. E. F. Redish Spring 2011 Exam 1 If you need more space, continue on the back and check here. 2. (25 points) A. (10 pts) My garage has an automatic garage door opener that goes up and down at the click of a button. In order to protect against the door smashing closed on someone or something, there is a box containing an infrared bulb on one side of the door near the floor and an infrared detector on the other side of the door near the floor. If the beam is unbroken by an object, the detector detects the beam of light and knows the path is clear. If there is something in the way, it blocks the light and the detector sends the door a signal not to go down. Both the bulb and the detector are enclosed in housings (metal boxes with a hole) that lets a beam of infrared light out/in. The detector is fixed in place, but the bulb can be adjusted up and down slightly by a spring-and-screw arrangement as shown above left. Suppose that the housings (boxes shown as lines) have not been installed at exactly the right heights and the beam from the bulb hits the detector at a point above the entry hole (at the arrow in the figure at the right). I can’t move the detector easily because both positioning screws have to be turned at the same time. To get the beam into the detector, should the screw on the bulb be adjusted to raise or lower the bulb? Explain your reasoning. (A diagram helps – but is not sufficient.) B. (15 points) A small object is viewed in a curved spherical mirror as shown in the figure below. Construct a careful ray diagram to determine where the image of the object will appear to be when viewed in the mirror. The small circle on the right represent the position of the center of the sphere of which the mirror is a part. Is the image real____ or virtual_____? (Check one)NAME___________________________________________ POINTS_______ Physics 122 Dr. E. F. Redish Spring 2011 Exam 1 If you need more space, continue on the back and check here. 3. (15 points) A common scam used to separate suckers from their money is the Ponzi scheme. People pay money in and then get their money back from people who put money in at a later time. If the number of people grows, early investors get back more money than they put in – sometimes by a lot. This works until all the people who are willing to put money in are used up. Then those who put money in but haven’t yet gotten anything back are shafted. Analyzing this in detail is too complex for an exam question, but let’s get an estimation of an example that at least shows the Ponzi principle: If you get in late, you lose. A chain letter is a kind of Ponzi scheme. Each person who gets one is supposed to send a copy of the letter to 4 people and asks each of them to send it to 4 more, etc. (For this
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