Physics 113 Exam #4 Angular momentum, static equilibrium, universal gravitation, fluid mechanics, oscillatory motion (first part)

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1 Physics 113 Exam #4 Angular momentum, static equilibrium, universal gravitation, fluid mechanics, oscillatory motion (first part) Answer all questions on this examination. You must show all equations, show all work and explicitly state all assumptions to receive full credit. Credit will not be given for work not shown. If the answer is not unitless, be sure to state the units as part of the answer. If dimensional analysis is required to solve the problem, be sure to show how you did it. If you use trigonometric functions, be sure to draw a figure showing the relevant triangles (sides and angles) involved. Remember to consider significant figures. Make sure that you clearly show your process and the reasons behind each step in your process, so that you can earn more partial credit. The backs of the question sheets are available for solving problems or for scribbling notes. Constants and equations that you might find useful are provided on a separate handout. Please do not write on that handout. You must turn in your exam at 9:55 am, so the next class can assemble. When you are finished, please turn this examination in to the professor or proctor. Wake Forest University is an academic community that subscribes to an honor system. By accepting membership in this community, each student assumes the obligation to be trustworthy in all pursuits. I have neither given nor received aid on this examination. Printed name: Signature: Question 1. Multiple choice questions please circle the correct answer. Be sure to circle clearly just one answer. (18 points total; 2 points each) a. A competitive diver leaves the diving board and falls toward the water with his body straight and rotating slowly. As he falls, he pulls his arms and legs into a tight tuck position, rotating as shown in the figure. What happens to his angular speed? Increases Decreases Stays the same Impossible to determine b. Consider the same diver as above. What happens to the rotational kinetic energy of his body when he moves into the tuck position? Increases Decreases Stays the same Impossible to determine Page 1

2 c. Consider the same diver. What is the direction of this same diver s angular momentum? Upward Downward Out of the page Into the page d. The pressure at the bottom of a filled glass of water ( ρ = 1000 kg/m 3 ) is P. The water is poured out and the glass is filled to the same level with ethyl alcohol (ρ = 806 kg/m 3 ). Which of the following best describes the pressure at the bottom of the glass? Equal to P Larger than P Smaller than P Impossible to determine e. You observe two helium balloons floating next to each other at the ends of strings secured to a table. The facing surfaces of the balloons are separated by 1-2 cm. You blow through the small space between the balloons. What happens to the balloons? They move away from each other. They are unaffected. They move toward each other. f. An apple is held completely submerged just below the surface of water in a container. The apple is then moved to a deeper point in the water. Compared with the force needed to hold the apple just below the surface, what is the force needed to hold it at the deeper point? Smaller Larger The same Impossible to determine g. Which of the following statements is true about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors? A X B could be larger than AB A X B could be smaller than AB A X B is equal to AB None of these answers is correct. Page 2

3 h. A block on the end of a spring is pulled from its equilibrium position (x=0) to a position x=a and it is released at time t=0. In one full cycle of its motion, through what total distance does it travel? A/2 A 2A 4A None of these answers is correct. i. Consider the same block as the previous question. If the phase constant for this same block on the end of the spring is 0, what is the position of the block at time t=0? A/2 A 2A 4A None of these answers is correct. Question 2. (9 points; 4 for each numerical answer and one for the explanation.) Calculate your weight two different ways using Newton s universal law of gravitation and Newton s second law. Compare your two answers. If both methods gave you the same answer, explain why. If the methods gave you different answers, explain why. Page 3

4 Question 3. (6 points; 2 points each) A satellite originally moves in a circular orbit of radius R around the Earth. Suppose it is moved into a circular orbit of radius 4R. Answer these three questions about the satellite. Select your answer from the list on the right and mark the letter of the answer in the space provided. What does the gravitational force exerted on the satellite become at the new orbit? What happens to the speed of the satellite? What happens to its period? a. 16 times larger b. 8 times larger c. 4 times larger d. 2 times larger e. unchanged f. 1/2 as large g. 1/4 as large h. 1/8 as large i. 1/16 as large Question 4. (6 points; 3 points each) Two vectors are given by vector A = (-2 î + 5 ĵ ) and vector B = (3 î + 2 ĵ ). a. Find A X B. b. Find the angle between A and B. Page 4

5 Question 5. (9 points; 3 points each) After our sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now, but a radius equal to the radius of the earth. Calculate the following: a. The average density of this white dwarf. b. The free-fall acceleration at its surface. c. The gravitational potential energy of a 1.00 kg object at its surface. Page 5

6 Question 6. (8 points; 4 points each) Assume that Young's Modulus for bone is 1.50 x N/m 2 and that the bone will fracture if more than 1.50 x 10 8 N/m 2 of pressure is exerted. a. What is the maximum compressive force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.60 cm? b. If a force of this magnitude is applied compressively, by how much does the 22.0 cm long bone shorten? Page 6

7 Question 7. (14 points; 5 points for FBD and 8 points for three equations and terms) A ladder is leaning against a wall, as shown in the picture. a. Draw a free body diagram for the ladder. Describe each force as the type of force, its origin, and what the force is acting on. b. Write the complete equations that must be satisfied for the ladder to be at equilibrium: ΣF y, ΣF x, Στ. (Be explicit in defining any terms or stating any assumptions necessary to write these equations.) Page 7

8 Question 8. (10 points; 4 points each for a and b, 2 points for c) Model the Earth as a uniform sphere. a. Calculate the angular momentum of the Earth due to its spinning motion (rotation) about its axis. (Full credit requires giving both the magnitude and direction of the momentum. Give the direction in terms of geographical locations, i.e. up or down are not a good answers. You may draw a sketch to justify your answer for the direction.) b. Calculate the angular momentum of the Earth due to its orbital motion (revolution) about the Sun. (Full credit requires giving both the magnitude and direction of the momentum. Give the direction in terms of geographical locations, i.e. up or down are not good answers. You may draw a sketch to justify your answer for the direction.) c. Compare the two quantities of angular momentum. Which is larger in magnitude? Page 8

9 Question 9. (4 points) The figure shows overhead views of a uniform disk that can move linearly or rotate about its center. Three forces of magnitudes F, 2F and 3F act on the disk, either in the center, on the rim or halfway in between as shown. Which disks (if any) are in equilibrium? e. None of these disks is in equilibrium. Question 10. (8 points) In a hurricane, the air (density = 1.29 kg/m 3 ) is blowing over the flat roof of a shed at a speed of 120 km/hr. If the roof area is 110 m 2, what is the lifting force on the roof? Page 9

10 Question 11. (8 points) A 6 kg mass is suspended by a string so that it is submerged beneath a liquid of unknown density. The tension in the string is measured to be 45 N. Find the ratio of the liquid density to the density of the submerged mass. (Work through the equations first, and then include numbers. For full credit, you will arrive at a numerical answer for this question.) If you are finished, go back to each of the questions and make sure you answered the questions that were asked. Don t make this test harder than it is. Page 10

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