In this exam. Define g as a positive number. If a numerical answer...

NAME_________________________FINAL P113 fall 09 10 pages+ 11 pages formulas.

Prof. Aran Garcia Bellido, Prof. Arie Bodek PHY113 Fall 09 – FINAL

Hubbell Auditorium HUTCH 141 NAME(print) :___________________ID #______________________________ Signature: _____________________________ Workshop TA:______________________ Workshop Day/Time_________________________________________ Exams will be available from the office of Prof. Garcia-Bellido (B&L 314) after Jan. 13. In this exam. Define g as a positive number. If a numerical answer is needed, you may use g=10 m/s2 THERE SHOULD BE 10 Pages plus formula sheets separately (for a total of 21 pages) Complete the information above, but DO NOT TURN THE PAGES UNTIL YOU ARE INSTRUCTED TO DO SO. You are responsible for reading the rules carefully before you begin. Exam rules: You may use only writing instruments while taking this test. You may not consult any calculators, computers, books, notes or each other. A formula sheet is a separate handout. NOTE THAT CALCULATORS ARE NOT NEEDED. Answer the multiple choice questions by circling one answer. For each multiple choice question, select only one answer. Questions with more than one answer will be considered incorrect. There is no partial credit for the multiple choice questions. For non-multiple choice problems, the answers need to be well motivated and expressed in terms of the variables used in the problem. Use the blank spaces provided, or refer to the back of the page if you need more space. You will receive partial credit when appropriate, but only if we can read your solutions. Answers that are not motivated will not receive any credit even if correct. Questions with more than one answer will be considered incorrect. If you want to redo a problem, please cross out the previous solution. General Word of advice, it is useful draw a picture if you can whenever you start to solve a problem in any field. In general, express your answers in terms of variables, check the dimensions of your answer, and plug in values for special cases. Grader Problem Score Max TA1 I ___________ 25% TA2 II ___________ 25% TA3 III __________ 25% TA4 IV __________ 25% Total __________ 100% Note to graders. Check the back of each page as well as the back of the previous page. Cross out with pen every blank page, and any blank section on the back of every page to make sure that you do not miss anything.


Problem 1-Grader : TA1__________Score__________ _/25% Problem 1 25% : (Each part is an independent question) (You may continue your solution on the back of this page if needed.) You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions.

1A: 4% (Justify your answer in one line)

Two identical cylindrical disks have a common axis. Initially one of the disks is spinning. When the two disks are brought into contact, they stick together. Which of the following is true? a) The total kinetic energy and the total angular momentum are unchanged from their initial values. b) Both the total kinetic energy and the total angular momentum are reduced to half of their original values. c) The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value. d) The total angular momentum is reduced to half its original value, but the total kinetic energy is unchanged e) The total angular momentum is unchanged, and the total kinetic energy is reduced to one-quarter of its original value. justification:

(a) lB: 4%: (Justify your answer in one line) An 80-kg man on ice skates pushes a 40-kg boy, also on skates, with a force of 100 N. The force of the boy on the man is a) 200 N. b) 100 N. c) 392 N. d) 784 N. e) zero unless the boy pushes back. justification:


Grader TA1 problem 1 continued (Each part is an independent question) (You may continue your solution on the back of page) SHOW YOUR WORK You may assume g=+10 m/s2 in this exam 1 C: 17% Two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on m4 from the three other spheres is zero. What is (how large is) M in terms of m? (Hint: the three angles in a triangle add up to 180 degrees).


Problem 2-Grader TA2 Score___________/25%_ Problem 2 25% : (Each part is an independent question) (You may continue your solution on the back of this page) You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions. 2A: 4% (Justify your answer in one line) The moment of inertia of a set of dumbbells, considered as two point masses M separated by a distance 2L, about the axis AA, is a) (1/2)ML2 b) ML2 c) 2ML2 d) (1/4)ML2 e) 4ML2

justification: 2B: 4% (Justify your answer in one line) In which direction is pressure by a fluid exerted on an object that is submerged in it. a) Perpendicular to all surfaces of the object b) upward c) parallel to the vertical surfaces, perpendicular to the horizontal surfaces d) downward e) None of the above justification:

A

A

M M

L L


Grader TA2 Problem 2 continued (You may continue your solution on the back of page) SHOW YOUR WORK You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions.) Problem 2C: 17%: Express you answer in terms of variables first , Check your dimensions, and plug numbers at the end. Two identical masses are hung on strings of the same length. One mass is released from a height h = 0.2 meters above its free-hanging position and strikes the second mass. The two masses stick together when they collide and move off. To what height H do the two masses rise after the collision? (Assume the heights are measured with respect to the relevant center of masses. That is to say, do not worry about the size of the balls relative to the height measurements.)


Problem 3 25% : . (Each part is an independent question) (You may continue your solution on the back of page) You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions. 3A: 4% (Justify your answer in one line) If two identical waves with the same phase are added, the result is a) a wave with the same frequency but twice the amplitude. b) a wave with the same amplitude but twice the frequency. c) a wave with zero amplitude. d) a wave with zero frequency. e) This problem cannot be solved without knowing the wavelength. justification:

3B: 4% (Justify your answer in one line) The torque exerted on a spinning, perfectly spherical and uniform density orbiting communications satellite by the gravitational pull of the earth is a) directed toward the earth. b) the cause of satellite precession toward the earth. c) directed parallel to the earth's axis of rotation and toward the north pole. d) directed toward the satellite. e) zero. justification:


Problem 3 continued Grader : TA3 ______ (Each part is different questions) (You may continue your solution on the back of page) SHOW YOUR WORK 3C: 17 % Express your answer in terms of variables first, check your dimensions, and plug numbers at the end. The brothers of the I Luv To play fraternity recently decided to create an outdoor study center on the second floor deck of their fraternity house. Of course, the first thing such a study center needs is a hot tub! So, the brothers bought a hot tub with a mass of M=200 kg and pulled it up a θ = 45 degree ramp to the second floor deck which is h=5 m above the ground. The coefficient of kinetic friction of the tub on the ramp surface was µk=0.1. a) What is the total work (W1) done by the boys as they pulled the hot tub up the ramp, assuming the tub was pulled up slowly with constant velocity? One of the brothers, Pervis Pinhead, was taking physics 113 at the time. He told his brothers that they would have to do less work if they moved the hot tub up in less time. Let's see if this is true. b) How much mechanical work W2 would the brothers have done on the hot tub if they moved it up the ramp with a constant acceleration of a =0.2 m/s2?


Problem 4-Grader TA4 Score_____________ /25%_ Problem 4 25% : (Each part is an independent question) (You may continue your solution on the back of page) You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions. 4A: 4% (Justify your answer in one line) The fundamental frequency of a vibrating string (fixed at both ends) is f. If the tension in the string is doubled, the fundamental frequency becomes a) f/2 b)

€

f/ 2 c) f d) 2 f e)

€

2/f justification: 4B: 4% (Justify your answer in one line) A stationary block with mass 3m sits on a frictionless surface. It is attached via massless cords, as shown below, to two blocks of mass m. The pulleys are massless and frictionless. The tension in the cord at point A is a) zero. b) 5mg. c) 2mg. d) mg. e) 4mg. justification:

m m

3mm

A 3m


Problem 4 continued GRADER TA4_____________ (You may continue your solution on the back of page) SHOW YOUR WORK You may assume g=+10 m/s2 in this exam. Express your answers in terms of variables and plug numbers at the end. Check your dimensions. 4C: 17%: --- A player hits a baseball at a height y0 =h above the ground at an angle θ with respect to the horizontal. In order to hit a home run, he must clear the fence which y1=h meters high and a distanced R away. You may neglect air resistance

4C –a 7%-- Case (a) - With what speed V0 must the player hit the ball if he is to clear a fence with a height y1=h (which is the same height that he hits the ball above the ground) ? Derive the expression (express your answer in terms of R, g , and θ). (Do not just use the range formula). – you may neglect air resistance.

(You may continue your solution on the back of page) SHOW YOUR WORK Case (a) y0 =h y1=h R

V0=?

y1=h

θ


NAME:________________ Back of this page and previous page checked?________ EXAM Problem 4 continued Grader TA4: ____________________ 4C-b 10%-- Case (b) With what velocity V0 must the player hit the ball if he is to clear a fence with a height y1 =h+Δ ? (express your answer in terms of R, g , Δ and θ) Case (b) y0 =h

R

V0=?

y1 =h+Δ

θ

In this exam. Define g as a positive number. If a numerical answer...

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