Physics 101 Fall 2005: Test 1 Free Response and Instructions

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1 Last Name: First Name: Physics 101 Fall 2005: Test 1 Free Response and Instructions Print your LAST and FIRST name on the front of your blue book, on this question sheet, the multiplechoice question sheet and the multiple-choice answer sheet. TIME ALLOWED 90 MINUTES The test consists of four free-response questions and ten multiple-choice questions. The test is graded on a scale of 100 points; the first free-response question accounts for 15 points, the second for 15 points, the third for 20 points, the fourth for 20 and the multiple-choice questions account for 30 points. Answer the four free-response questions in your blue book. Answer the multiple-choice questions by marking a dark X in the appropriate column and row in the table on the multiple-choice answer sheet. Consult no books or notes of any kind. You may use a hand-held calculator in non-graphing, nonprogrammed mode. Do NOT take test materials outside of the class at any time. Return this question sheet along with your blue book and multiple-choice question sheet. Write and sign the Pledge on the front of your blue book. Show your work for the free-response problems, including neat and clearly labelled figures, in your blue book. It is possible that answers without explanation (even correct answers) will not be given credit. Take g = 9.8 m/s 2 or 32 ft/s (15 pts) A model rocket has a constant vertical acceleration of 40.0 m/s 2 while its engine is running. The rocket is fired vertically, and the engine runs for 2.5 s before it uses up all the fuel. After the engine stops, the rocket continues as a free particle until it reaches the ground. Assume the rocket is initially at rest on the ground. Calculate (a) the highest point the rocket reaches, (b) the total time the rocket is in the air, (c) the speed of the rocket just before it hits the ground. 2. (15 pts) As your jet plane accelerates down the runway during takeoff, you decide to determine its acceleration which is constant. To do this you take out a plumb bob, i.e., a mass on the end of a light string, and suspend it. You note that instead of hanging vertically, its string makes a constant angle of θ with respect to the vertical as shown in the figure below. (a) Draw and label a free-body-diagram for the plumb bob. (b) Derive an expression for the acceleration of the plane in terms of g and θ. (c) If the mass of the bob is m, what is the tension in the string? Figure 1: Problem 2

2 October 4, 2005 PHYS101 Test 1 - Free Response Section Page 2 3. (20 pts) A whale traveling southwest at 7.0 km/hr is spotted 5 km to the northwest off the coast of Malibu. Photographers jump into a boat that can move at 30 km/hr. (a) With what velocity will the photographers intercept the whale assuming that their boat travels a straight-line path? (b) What is the position vector of the whale from the original point on the coast when the photographers reach the whale? 4. (20 pts) A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/hr, the rocket is dropped. After the drop, the airliner maintains the same altitude and speed and continues to fly in a straight line. The rocket falls for a brief time, after which its rocket motor turns on. Once its motor is on, the combined effects of thrust and gravity give the rocket a constant acceleration of magnitude 3g directed at an angle of 30 above the horizontal. For safety reasons, it is arranged that the rocket passes 1 km in front of the airliner when it climbs through the airliner s altitude. Ignore air resistance. (a) Sketch a x vs. t graph showing the motions of both the rocket and the airliner (on the same graph). (b) Sketch a y vs. t graph showing the motions of both the rocket and the airliner (on the same graph). (c) What is the time interval between the firing of the rocket and it passing 1 km in front of the airliner?

3 Last Name: First Name: Physics 101 Fall 2005: Test 1 Multiple-Choice Questions 1. A woman swings a stone attached to a rope in a horizontal circle at constant speed. The figure below represents the path of the rock looking down from above moving in a counter-clockwise direction. Which vector could represent the acceleration? 2. Assume that the new Ford Mustang accelerates uniformly from 80 km/h (50 mi/h) at t = 0 to 113 km/h (70 mi/hr) at t = 9 s. Which of the following graphs below best describes the motion of the car?

4 October 4, 2005 PHYS101 Test 1 - Multiple-Choice Section Page 4 3. In which case does block m experience a larger acceleration? In case (1) there is a 10 kg mass hanging from a rope and falling with constant acceleration. In case (2) a hand is providing a constant downward force of 98 N. Take g = 9.8 m/s 2. Assume massless ropes and frictionless surfaces. (a) case 1. (b) both cases are the same. (c) depends on the value of m (d) case 2. Refer to the figure below for questions 4 and Which of the position versus time curves in the figure above best shows the motion of an object of mass m under the influence of a constant resultant force that acts in the +x direction? (a) a (b) b (c) c (d) d (e) e 5. Which of the position versus time curves in the figure above best shows the motion of an object with non-zero speed, but zero acceleration? (a) a (b) b (c) c (d) d (e) e

5 October 4, 2005 PHYS101 Test 1 - Multiple-Choice Section Page 5 Refer to the figure below for questions 6 and 7. The figure below represents the positions of two blocks of equal mass at successive 0.1 s time intervals. The blocks are moving to the right. 6. The magnitude of the resultant forces acting on the blocks are related as follows: (a) The magnitude of the resultant force on block A is greater than the magnitude of the resultant force acting on block B. (b) The magnitude of the resultant force on block A is equal to the magnitude of the resultant force acting on block B, and both resultant forces are not zero. (c) The magnitude of the resultant force on block A is equal to the magnitude of the resultant force acting on block B, and both resultant forces are zero. (d) The magnitude of the resultant force on block B is greater than the magnitude of the resultant force acting on block A. 7. Do the blocks ever have the same speed? (a) No. (b) Yes, at instant 1. (c) Yes, at instant 3. (d) Yes, at instant 4. (e) Yes, at some time during the interval 3 to A force F acts on mass m 1 giving it an acceleration a 1. The same force acts on a different mass m 2 giving it an acceleration a 2 = 2 a 1. If m 1 and m 2 are glued together and the same force F acts on this combination, what is the resulting acceleration? (a) 3 4 a (b) 3 2 a (c) 1 2 a (d) 2 3 a (e) 4 3 a

6 October 4, 2005 PHYS101 Test 1 - Multiple-Choice Section Page 6 9. The figure below shows the trajectory of a ball kicked three different times. For each case, the ball rises to the same height h as indicated in the figure. For which case is the ball launched with the greatest speed? (a) Case 1 (b) Case 2 (c) Case 3 (d) They are all launched with the same speed. 10. Two people (labelled P and Q) are on escalators, both inclined at 45 to the horizontal. P is moving down the escalator at a constant speed and Q is moving up the other escalator at the same constant speed. Of the vectors shown, the one that best represents the velocity of Q with respect to P is

7 Last Name: First Name: Physics 101 Fall 2005: Test 1 Multiple-Choice Answers A B C D E