sp07m3Soln - Physics 140 Spring 2007 Midterm 3

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Unformatted text preview: Physics 140 Spring 2007 Midterm 3 ‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘ w? if :r a? is 1. (P) uniform bowling ball of diameter 26 cm is initially at rest at the top of a ramp “ WM inclinEd‘37“%‘"‘a“bove horizontal. You give it a gentle nudge, and it begins to roll without slipping down the ramp. At what distance along the ramp will the ball’s angular velocity reach 20 rad/s? mi 5 :5 uniform door of mass M and width L. The diagram below shows the view looking down from above the door (i.e., gravity acts into the page) and the bullet’s velocity is perpendicular to the door’s initial orientation. If the hinge is frictionless, what is the final angular velocity u) of the door and bullet after they collide? Kymvd/ (ML2 + 3de) ) 2mvd/ (ML2 + 2md2) c) nivd/(ML2~md2) d) mv/(MLZ + ma?) e) mvdz/(MLZ +md2) Physics 140 Spring 2007 Midterm 3 3. (P) A uniform rod of length L, hinged about its lower end (0), is held at an angle 8 above horizontal and released from rest, as shown at left. As the rod passes through the horizontal, what is the tangential acceleration experienced by its outer tip (the end opposite the hinge)? orbiting planet Xanadu, a planet of radius rX with an escape velocity, vmzl34 m/s. The ship’s engineer is asked to calculate the work needed from the ship’s engines to move the ship from a stable circular orbit of radius er to one of radius 6rx. What is the correct answer to this question? ,MW 5'” afléQxW J “"“’”B) 7.6x109J c) 8.8x109J d) 9.9x109J 9e) 1.4x1010J Physics 140 Spring 2007 Midterm 3 5. (P) When drilling a 12.7—mm-diameter hole in a thick aluminum sheet, a certain shop manual recommends a drill speed of 1250 rev/min. If a drill bit of this size spins at the recommended speed, what is the maximum centripetal acceleration, in units of g, experienced by any part of the bit? $2,, : air“ ‘“ rt wig c) 17g , ‘ e) 42g “W52” ~ its” [ 6. (P) The simple yo—yo pictured below consists of a light (massless) string wrapped around a thin—walled cylinder of radius R. The yo—yo is released from rest. What is the angular acceleration of the cylinder after it is released? fiQg/ZR "“ b) 3g/2R w c) g/R d) ZgR e) g/2 Physics 140 Spring 2007 Midterm 3 7. A 30 kg plank, of length I = 8m, rests on the ground and on a frictionless roller at the top of a wall of height h = 4 m (see figure). The center of gravity of the plank is at its midpoint. The plank is in equilibrium if 6 2 70°, but slips if 9 < 70°. What is the coefficient of static friction between the plank and the ground? (flat: the contact force at the roller is normal to the plank.) d A m2, and coin system after the coin is added? , W“ F” 1“ D a) 60 rev/min :90; 54 rev/ min i rev/min 4O rev/ min e) 30 rev/ min MP Physics 140 Spring 2007 Midterm 3 9. Which of the following statements best explains why astronaut Wendy Lawrence orbiting Earth on Space Shuttle mission STS-l 14 is apparently weightless? a) The orbit is circular and not elliptical. She is far enough away from earth and does not experience a gravitational force. aggwflhe radial acceleration towards the center of the earth is equal to the acceleration of gravity at the position of the spacecraft. d) The radial acceleration towards the center of the earth is equal and opposite to the acceleration of gravity at the position of the spacecraft. e) There is no air in the spacecraft. 10. Two identical, uniform marbles, each of mass M and radius R, are confined within a smooth cylinder of diameter 3R, shown in cross—section in the diagram below. If the marbles are in static equilibrium, which of the following statements is false? M1: The normal force at point B equals ZMg. blfihe normal force at point A has larger magnitude than the normal force at point C. Wye) Each of the forces acting on the upper marble produces zero torque on that marble. d) The normal forces (n) at the contact point between the marbles form a Newton’s third— law pair. e) The weight of each marble acts at its geometric center. r Physics 140 Spring 2007 Midterm 3 11. The Earth has two rotational kinetic energies, Espin and Eorb, associated with its daily spin on its axis and its annual, nearly circular orbit around the sun, respectively. Treating the Earth as a uniform sphere of radius REanh = 6.38x106 m rotating once per day, and assuming that it takes 365.25 days to orbit the Sun at a distance Rom: 1.50x10]1 Hi, what is the ratio, Espin/ Eorb, of the energy in daily spin to that in orbital motion? g: 5 fiat a) 1.35 x103 b) 2.89 x101 c) 3.24x10—2 d) 5.30 x10'3 We) 9 5x10-5 I "twwwm 12. A particular femur, a leg bone, has Young’s modulus Y=9.4x1011 Pa and minimum cross—sectional area 4.5x10‘4 m2. A compressional force in excess of 7.0><lO4 N will fracture this bone. What is the (linear) strain that would exist under this maximum stress? a) 3.0 xiO‘3 flemtfl xlO‘4 5.3 xlO"5 M d) 6.2 x10-6 e) 7.8 x10-7 Physics 140 Spring 2007 Midterm 3 13. A lightweight, rigid board is placed across two scales (A and B below) that are separated by a distance of 1.80 m. After a heavy crate of Sicilian salamis is placed on the board, scale A reads 452 N while scale B reads 341 N. Neglecting the mass of the board, how far from the left edge, x, was the crate placed? a) 0.532m b 0.695m (:5 .774m d) 0.934m e) 1.22m 14. Two eggs of equal mass are tossed into the air and follow the pair of trajectories (A and B) below. Calculated about the launch point P, what can be said about the nlaggtude of the torque 1: due to gravity on each egg at the apex (high point) of their “WW “trajectories? a) 1: (egg A) is greater than t (egg B) h‘ T (egg A) is equal to 1‘ (egg B) a g c) m (egg A) is less than 1? (egg B) i ‘‘‘‘ more information is needed 6) oh, no! not another #$%*ing egg toss question! Physics 140 Spring 2007 Midterm 3 15. (P) A yo~yo of mass m is placed on a horizontal table, with static friction coefficient us between the two. In the three cases shown below, the string of the yo—yo is pulled gently, with force F < us mg, in the direction shown. In which case(s) will the yo~yo initially roll to the right? a) A b) B c) C d both B and C 16. Planet Vulcan has 4 times the mass of Earth, yet it has the same gravitational acceleration on its surface as we do on Earth. Assuming both planets to be spherical and of uniform density, what can we say about the size of Vulcan relative to Earth? W; 53% a) Vulcan’s diameter is 1/2. of Earth. My} EQWVulcan diameter equals that of Earth. m Wulcan’s diameter is 2 times that of Earth. M d) Vulcan’s diameter is 4 times that of Earth. xi e) Vulcan’s diameter is 8 times that of Earth. Physics 140 Spring 2007 Midterm 3 17. (P) A solid sphere, hollow sphere and a ring roll the same distance down a curved incline and are launched horizontally into the air at a height H above the ground. Rank the objects in order of the horizontal distance x that they will travel before hitting the ground, smallest LWL Wm M,“ WW é,» “wiring, hollow sphere, solid sphere b) solid sphere, ring, hollow sphere c) hollow sphere, solid sphere, ring m (1) solid sphere, hollow sphere, ring e) ring, solid sphere, hollow sphere 18. (P) Two stars, each of mass m, are diametrically opposed as they rotate about each other in uniform Circular motion, always with separation d as drawn. Measured in the center—of~mass frame, what is the total angular momentum of this binary star system? Gm d) 2 “21’3" W5 Gm3d 2 Physics 140 Spring 2007 Midterm 3 19. A bicycle wheel is spinning on an axle that you holding in your hands (the top of the wheel is rotating towards you). You exert a clockwise torque on the axle by pulling your left hand up and your right hand down, as indicated by the forces F in the figure. From this torque, in what direction will the axle tend to rotate? wheel rotation a) The axle will not rotate at all. uch that the right side of the axle moves down and the left side moves up. I ch that the right side of the axle moves into the page and the left side moves out. w (1) Such that the right side of the axle moves up and the left side moves down. e) Such that the right side of the axle moves out of the page and the left side moves in. 20. (P) What is the correct ordering of the moments of inertia I A, 113, and 1C for rotational motion of a thin square slab about respective axes A, B, and C indicated below? a) IB>IA>IC if?”va b) Ic>IB>IA C) IA>IB>IC @IC>IA>IB e) [B > [C > [A "N gt éé‘w Physics 140 Spring 2007 Midterm 3 21. (Bonus!) Dark energy makes up approximately what percentage of the overall energy density of the universe? a) 2% b) 26% %SO% / W76% “Mm 99.97% 11 ...
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sp07m3Soln - Physics 140 Spring 2007 Midterm 3

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