EXAM I Phys 172H Fall 2009 Modern Mechanics - Honors Instructor: Prof. E. W. Carlson

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1 EXAM I Phys 172H Fall 2009 Modern Mechanics - Honors Instructor: Prof. E. W. Carlson TEST FORM A There are two parts to Exam I: The machine-graded part of this test, and the last page that you turn in to be graded by hand. Machine Answer Sheet (This part of the exam is worth 75 points.) Using a pencil, fill in Last Name, First Name, and Middle Initial, plus your 10-digit Purdue University ID number, which starts with 00. Enter Carlson for instructor, Course (PHYS 172H), Date (9/17/09), and Test (1). Enter Test Form from the box above. Leave Section blank. You must include your Signature. Fill in only one answer per question. If your answer is slightly different, choose the closest answer. You must use a PENCIL and fill in the circle completely. Hand-Graded Part: (This part of the exam is worth 25 points.) Enter Name, Signature, PUID. Your work must be legible and clear Correct reasoning is required for full credit -- a correct answer with incorrect or no reasoning will be counted as wrong. Cross out anything you do not want us to read in the hand-graded part. FINISHED? Turn in all parts of this exam to the front of the classroom, including question sheets and scratch paper. Show ID to the instructor or teaching assistant when turning in your exam.

2 Each multiple choice question is worth 5 points. Problem 1. Vectors. Which statement is true about these vectors? 1) 2) CORRECT 3) 4)

3 Problem 2. Carnival Game. To win the the following carnival game, you must throw a ball such that it goes through the cylinder on the left without touching the sides at all. That is, the ball must land in the cylinder with no horizontal component to its velocity. B A C Carnival Game At what angle should you throw the ball in order to win the game and take home the giant teddy bear? (Neglect air resistance.) CORRECT 1) Steeper than 45 O 2) 45 O 3) Less steep than 45 O 4) This game is a scam, since it is not possible to win.

4 Problems 3 and 4 are about the Earth and Moon. (Not to scale) m Eearth =6.0 x kg mass R Earth = 6.4 km radius m Moon = 7.3 x kg R Moon = 1.7 km R E-M = 380,000 km Earth-moon distance Problem 3. What is the magnitude of the force of gravity that the Moon exerts on the Earth? CORRECT 1) 2.0 x N 2) 5.6 x N 3) 8.4 x N 4) -1.2 x N Problem 4. How many electrons would you have to move from the Earth to the Moon for the magnitude of the electric force between the Earth and Moon to equal that of the gravitational force between them? Choose the closest answer. (There are about electrons in all of the atoms on Planet Earth.) 1) 10 electrons 2) electrons CORRECT 3) electrons 4) electrons

5 Problem 5. A stationary particle in otherwise empty space decays into two fragments. One of the fragments is obsesrved to have a momentum of <5.6, -4.3, 2.0> kg m/s just after the decay. The other particle is invisible to the detector and so its momentum cannot be directly measured. What is the momentum of the invisible particle? 1. <5.6, -4.3, 2.0> kg m/s CORRECT 2. <-5.6, 4.3, -2.0> kg m/s 3. <5.6, 4.3, -2.0> kg m/s 4. <-5.6, -4.3, 2.0> kg m/s 5. Not enough information is given

6 Problems 6-8 are about four bees, with the following velocities: Bee A: <0,1,1> m/s Bee B: <1,0,1> m/s Bee C: <0,3,3> m/s Bee D: <-1,1,1> m/s Problem 6. Which of the bees fly with the same velocity? 1) only A & C 2) only B & D 3) only A & D 4) A, B, & C CORRECT 5) None of the bees fly with the same velocity Problem 7. Which of the bees fly in the same direction? 1) only A & B CORRECT 2) only A & C 3) B, C, & D 4) None of the bees fly in the same direction Problem 8. Which of the bees fly with the same speed? 1) only C & D 2) only A & D CORRECT 3) only A & B 4) None of the bees fly with the same speed

7 Problems 9-11 are about the following scenario. The windshield of a speeding car hits a hovering insect. Problem 9. Compare the magnitude of the force that the car exerts on the bug to the force that the bug exerts on the car. (Note: the interatomic forces between bug and windshield are electric forces.) 1) The force that the car exerts on the bug is bigger. CORRECT 2) The two forces are equal. 3) The force that the bug exerts on the car is bigger. Problem 10. Compare the magnitude of the change of momentum of the bug to that of the car: CORRECT 1) The magnitudes of the change of momentum are equal. 2) The magnitude of change of momentum of the bug is bigger. 3) The magnitude of change of momentum of the car is bigger. Problem 11. Compare the magnitude of the change of velocity of the bug to that of the car: 1) The magnitudes of the change of velocity are equal. 2) The magnitude of change of velocity of the car is bigger. CORRECT 3) The magnitude of change of velocity of the bug is bigger.

8 Problems are about the following scenario. In outer space, far from other objects, block 1 of mass 45 kg is at position < 9, 8, 0 > m, and block 2 of mass 1100 kg is at position < 17, 8, 0 > m. Problem 12. What is the (vector) gravitational force acting on block 2 due to block 1? It helps to make a sketch of the situation. 1) <0, x 10-8, 0 > N 2) < 8.02 x 10-7, 0, 0 > N CORRECT 3) < x 10-8, 0, 0 > N 4) <0, 0, 8.02 x 10-7 > N Problem 13. At 4.2 seconds after noon both blocks were at rest at the positions given above. At 4.3 seconds after noon, what is the (vector) momentum of block 2? CORRECT 1) < x 10-9, 0, 0 > kg m/s 2) <0, 2.1 x 10-2, 0 > kg m/s 3) < 8.02 x 10-7, 0, 0 > kg m/s 4) < x 10-9, 8.02 x 10-7, 0 > kg m/s Problem 14. At 4.3 seconds after noon, what is the (vector) momentum of block 1? 1) < 2.1 x 10-2, 0, 0 > kg m/s 2) < 3.9 x 10-5, 0, 0 > kg m/s 3) <0, 7.09 x 10 8, 0 > kg m/s CORRECT 4) < 5.18 x 10-9, 0, 0 > kg m/s

9 Problem 15. A star of mass 7 x kg is located at <5 x 10 12, 2 x 10 12, 0> m. A planet of mass 3 x kg is located at <3 x 10 12, 4 x 10 12, 0> m and is moving with a velocity of <0.3 x 10 4, 1.5 x 10 4, 0> m/s. What is the initial force due to gravity of the star on the planet? 1) 9.2 x <0.7, -0.7,0> N 2) 9.2 x <-0.7, 0.7, 0> N CORRECT 3) 1.8 x <0.7, -0.7, 0> N 4) 1.8 x <-0.7, 0.7, 0> N

10 PHYS 172H -- Fall 2009 Name (Print): Signature: PUID: Problem 16. (Hand Graded, 15 total points) You jump off of a platform, and catch a ball in mid-air. Your center of mass is at initial position <0,0,0>m. Just after you leave the platform, your initial velocity is <12,5,0>m/s. Your friend throws you a ball of mass 2kg, and you catch it in mid-air, when the y-component of your position again reaches r y = 0m. The velocity of the ball right before you catch it is <0,0,22>m/s.

11 Name A) (5 points) What is your momentum just after you leave the platform? State your assumptions clearly. For the purposes of this problem, it is okay to lie about your own weight, but you should state a reasonable number.

12 Name B) (10 poins) What is your momentum just after you catch the ball?

13 Name C) (10 poins) Approximately how long was your friend s hand in contact with the ball in order to accelerate it to roughly 22m/s? State your assumptions and approximations clearly.

14 Constants and Equations v avg " r rf ri = # " t t t f i p = mv = 1 " v # 1$ % & ' c ( 2 v = p / m p " 1+ # $ % mc & 2 p = F t total ext, net p + p = 0 system surroundings v avg, x v = ix + v 2 fx m m F = G rˆ r 2 1 grav on 2by F = gm grav on mby M E F = 1 q q rˆ 2 1 elec on 2by " # 0 r2 # 1 F = k s spring S G = 6.7$ 10 0 # m/s Earth Earth electron proton neutron kg m 2 # kg # kg proton N?m N m 2 2 kg 1 9 N?m N m = 9$ " C c = $ g = 9.8 N/kg M R m m m = $ = $ = $ = $ % m 1 kg = 2.2 pounds 1 inch = 2.54 cm 1 foot = 30.5 cm 1 mile = 1609 m

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