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Unformatted text preview: NAME Recitation Instructor: Physics 112 Recitation Section #: December 13, 2004 Final Exam
3  5:30 PM PLEASE BE SURE THIS PACKET HAS 12 PAGES! (This includes the cover sheet and a scrap page.)
This packet contains 6 Short Answer Questions, 4 Problems, 2 pages of Possibly Useful Information, and a page of scrap paper near the end. You may also use the backs of pages for scrap. WORK ON SCRAP PAPER WILL NOT BE GRADED. Write your answers ON THESE QUESTION SHEETS in the spaces provided. For Short Answer Questions #16, ONLY ANSWERS WILL BE GRADED. For Problems #710, where algebra or computations are required, BE SURE YOUR METHOD OF SOLUTION IS CLEAR, and SHOW YOUR WORK in the spaces provided. If you need more space, use the backs of the question sheets and indicate the whereabouts of your work for each question. ANSWERS WITHOUT WORK will NOT receive credit (except for short answer questions). WORK ON SCRAP PAPER WILL NOT BE GRADED. Point values for questions are given below. BUDGET YOUR TIME. Don't spend too much time on any one question or part of a question. Answer those questions you can do easily first, and then return to the more difficult ones. It is valuable use of your time to READ THE ENTIRE EXAM before starting to work on it. This is a CLOSED BOOK and CLOSED NOTES exam. You may NOT use any other references or personal assistance. You MAY use a NONGRAPHING calculator. For Grading Only: (Do not write here.) 13 45 6 /14 /12 /14 7 8 9 10 TOTAL /15 /10 /15 /20 /100 NAME I. SHORT ANSWER [40 points] Please write your answers in the spaces provided. (A) < 1 (D) 10 (G) 300 (B) 1 (E) 30 (H) 1000 (C) 3 (F) 100 (K) > 1000 Answer: Position (cm) 1. [4 points] What is the approximate quality factor Q for this damped harmonic oscillation? 2 1.5 1 0.5 0 0.5 1 1.5 2 0 0.5 1 Time (s) 1.5 2 2. [4 points] A spool resting on a horizontal surface has a string wrapped around its axle, as shown. When the string is pulled, which way will the spool roll? (A) To the right () (B) To the left () (C) It won't roll. Answer: f 3. [6 points] A bowling ball starts vf sliding to the left () with speed vo on a horizontal surface without spinning. As the ball slides along the surface, it begins to spin, eventually rolling to the left Final without slipping with speed vf and angular speed f . The bowling ball's radius = R, mass = m, and moment of inertia about its centerofmass = ICM . Pull vo Initial Which of the following statements is/are true? Please list the letters for all that apply. (A) mv o = mvf + ICM f (B) 2 mvo = 2 mvf + 2 ICMf (C) mv oR = mvfR + ICM f (G) None of these are true.
1
2 (D) mv o =
2 (mv f) + (ICM f) 2 2 1 2 1 (E) (F) vo = Rf vf = Rf Answer: 2 NAME 4. [12 points] A spinning wheel of mass M and radius R is precessing freely on a fixed pivot, as shown. (a) (2 points) What is the direction of the net torque acting on the wheel about the pivot? (A) (B) (C) (D) Up A D (E) into the page (F) out of the page
Down R
Pivot (G) This net torque is zero. Answer: B M
Side View (b) (2 points) If the wheel is spinning counterclockwise ) as seen from point B at the right end of the axle, ( which way is the wheel precessing as seen from point A directly above the wheel? (A) (B) (C) More information is needed to determine this. True/False. Please circle your answers to these questions: (c) (2 points) To make the wheel precess slower, it should be made to spin slower about its axle. (d) (2 points) To make the wheel precess slower, an additional external force should push on point B at the end of the axle in a direction opposite to the direction that the axis is already precessing. (e) (2 points) To make the wheel precess slower, an additional force should push upward () on point B. (f) (2 points) To make the wheel precess slower, its axle should be tipped upward at an oblique angle with respect to horizontal. Answer: True False True False True False True False 3 NAME 5. [10 points] A puck of mass m is sliding with speed vo on a frictionless horizontal surface towards a puck of mass 2m initially at rest. The pucks collide, and afterwards the pucks are moving with speeds v1 and v2 , as shown. (a) (6 points) Which of the following statements is/are true? Please list the letters of all that apply. (A) v o = v1 + v2 (C) v o (E)
2 +y v1
After v2 +x (B) mv o = mv1 + 2mv2
2 vo
2 = v1 + v 2 2 (D) 2 mvo = 2 mv1 + 2 (2m)v2 (F) mv o = 2 2 mv2 1 2 1 2 1 m
Before 2m 45 mv o = 2 mv1 (G) None of these are true. Answer: (b) (4 points) The initial momentum vector p o of the puck of mass m before the collision is shown on the grid. On the grid draw and label this puck's final momentum vector p 1 after the collision and its change in momentum vector p 1 due to the collision, and show how these 3 vectors combine geometrically. Be sure that p 1 and p 1 have the proper magnitudes and directions relative to p o and to the collision diagram above. po 6. [4 points] An energetic monkey of mass m is standing on a ledge at a height D above the top of a platform of mass m attached to the top of an ideal massless spring of spring constant k that is also attached to the ground. The monkey leaps up off the ledge by height H and then drops freely down onto the platform, after which the spring compresses and then propels the monkey back upwards. The monkey leaves the platform when the platform returns to its original position, a distance D below the cliff. To what height H must the monkey first leap above the ledge in order to just barely reach the top of the cliff again after landing on the platform and being propelled back up? (A) 0 (E) 3D/2 (B) D/3 (F) 2D (C) D/2 (G) 3D (D) D (K) 4D Answer: 4 NAME PROBLEMS [60 points] Please be sure your method is clear, and show all your work. o 7. [15 points] A person of mass m is standing on the edge of a turntable rotating counterclockwise ( ) with angular speed o on a frictionless vertical axle fixed to the ground. The turntable is a solid disk of mass M and radius R. The person then leaps off the turntable with speed v measured relative to the ground at angle from the tangent to the turntable's edge. (a) (5 points) When the person leaps off the turntable, which of the following quantities is/are conserved? Please list the letters of all that apply. (A) Linear momentum of the person + turntable (B) Kinetic energy of the person + turntable M axle R m v Top View (C) Angular momentum of the turntable + person about the axle (D) Angular momentum of the turntable about the axle + linear momentum of the person (E) None of these are conserved. Answer: (b) (10 points) With what speed v (relative to the ground) should the person leap so that after the leap the turntable is rotating in the opposite direction ( ) at its original angular speed o? Your answer may contain m, M, R, o, and , and it should be simplified if possible. Please show your work. Answer: 5 NAME 8. [10 points] A small block of mass 1.0 kg is supported in equilibrium in air by a spherical balloon filled with helium gas. If the mass of the balloon's material is negligible, and the volume of the block is also negligible, what must be the diameter of the balloon (in m)? Please show your work, and be sure your method is clear. [Possibly useful information: density of air = 1.2 kg/m 3 density of helium = 0.17 kg/m ]
3 Answer: 6 NAME 9. [15 points] A hungry 25 kg monkey is climbing a 20 kg ladder to reach a 5 kg bunch of bananas at the ladder's top end. The ladder is 5.0 m long, and it rests against a frictionless wall with its upper end 4.0 m above the ground and its lower end 3.0 m from the base of the wall. What minimum coefficient of static friction between the ladder and ground will allow the monkey to climb all the way to the top of the ladder and pick up the bananas without the ladder slipping? Please show your work, including any diagrams you use, and be sure your method is clear. Answer: 7 NAME 10. [20 points] Two identical blocks, each of mass m, on a frictionless horizontal surface, are connected to 3 ideal massless springs having two different spring constants, k1 and k2, as shown. The springs are all at their unstretched lengths when the blocks are at their equilibrium positions. k1 m k2 m k1 D D The two blocks are then displaced from their equilibrium positions by the same distance D in opposite directions, as shown, and are then released from rest there at the same time. (a) (4 points) Draw a freebody diagram showing ALL the forces acting on the LEFT () block just after it is released. Be sure to identify each force by interaction and the body providing it. (b) (2 points) Just after the blocks are released, which two forces acting on the LEFT block are equal in magnitude? (c) (2 points) Why are these two forces (part b) equal in magnitude? (d) (4 points) Just after the blocks are released, what are the magnitude and direction of the net force acting on the LEFT block? Your magnitude may contain k1, k2, m, D, and constants such as g, and it should be simplified if possible. magnitude: direction: (CONTINUED on next page) 8 NAME (e) (5 points) Use Newton's 2nd Law to derive a differential equation for the instantaneous position x(t) of the LEFT block in its subsequent motion as a function of time t. Let the block's equilibrium position be x = 0, and let displacements to the right () of this be positive (+). Please show your work. Answer: (f) (3 points) Use your differential equation from above or some other line of reasoning to derive an expression for the frequency of the subsequent oscillation of the blocks. Your answer may contain k1, k2, m, and constants such as g, and it should be simplified if possible. Please be sure your method is clear. Answer: 9 NAME 10 NAME Possibly Useful Information:
dr v = dt r = v av = dv a = dt v = a av = v AB = v AC + v CB dv atan = dt v2 arad = R [ r ] = [ v t] a (t)2
1 v dt
r t a dt
v t vx(t) = vox + axt Use an inertial ref. frame. GMm Fg = = mg = w r2 F = kx keff = k1 + k2 x(t) = xo + voxt + 2 axt2 vx2(t) = vox2 + 2ax[x(t)  xo] F A on B =  F B on A f s s N fd = 2 CAv2
1 F = ma
f k = k N fd = bv 1 1 1 = k + k k eff 1 2 p2 1 K = 2 mv2 = 2 m Ug = mgy Fx = W = U = 1 F ds ds  F dE dW P = dt = dt = F v GMm Ug =  r 2 Us = 2 kx dM Fthrust = vex dt Mo v = vex ln M v Ao  vBo = vBf  vAf r CM = mi r i
M dU p = mv dx dp F ext = dt J = F dt = p m A  mB 2m B v Af = m + m vAo + m + m vBo A A B B 2m A m B  mA v Bf = m + m vAo + m + m vBo B B A A p total F ext v CM = M a CM = M  d v = dt = r (t) = o + t K = 2 I2 Ktot = 2 MvCM2 + 2 ICM2 Ug = MgyCM
1 1 1 atan d = dt = r (t) = o + ot + 2 t2 I = mi r i
2 1
2 2 arad = 2r
1 2(t) = o2 + 2[(t)  o] Iaxis = ICM + Md2 Irod center = 12 ML
1
2 Isolid disk = 2 MR
2 Isolid sphere = 5 MR 11 NAME dL dt = L = I L total = r CM M v CM + ICM x(t) = A cos(t + ) vmax = A x(t) = Ao et/ cos('t + ) 2m = b = r F L = r p = Fr = Fr L = pr = pr = d2x(t) =  2 x(t) dt2 amax = 2A ' = 1 o2  2 o precession = L
1 f = T 2 = 2f = T = = o = k m g L MgD I with fd =  bv A(o) o Q = T = 2 A d A(d) = o2Ad (o2  d2)2 + (2d/)2 x(t) = A(d) cos[dt + (d)] m = V dp dy =  g g = 9.8 N/kg = 9.8 m/s2 1 m = 3.28 ft 3.14 2 10 F p = A p  po = gh Av = constant p + gy + 2 v
1
2 = constant G = 6.67 x 1011 Nm2/kg2 1 lb = 4.45 N e 2.72 3 1/e 0.37 8 c = 3.0 x 108 m/s 1 atm = 1.0 10 N/m C = 2R A = R
2 5 2 A B = AB cos = AB = AB = AxBx + AyBy + AzBz A B = AB sin = AB = AB ax2 + bx + c = 0 x =  b b2  4ac 2a A = 4R
4 2 3 V = 3 R 12 ...
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This test prep was uploaded on 04/21/2008 for the course PHYS 1112 taught by Professor Leclair,a during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 LECLAIR,A
 Physics, mechanics

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