PHYS 125 Fall 2007 Exam 3 11/29/2007 - 1 - Form #1 Physics 125 Fall 2007: Exam #3 Form #1 Please print your name:_________________________________________ Please list your discussion section number:_________________________ Please list your discussion instructor:______________________________ Instructions • Fill in your name above. • Each exam will have a different version number which will need to be written in the area of the scantron marked “Form”. • Record all your answers on the answer sheet provided. • This will be a 1.5 hour, closed book exam. The exam includes 20 questions. • You may use three 3x5 note cards containing information you think might be useful. You can write on both sides of the card if you like. • This is a closed-book exam. You may use a calculator which is for numerical calculations only and not to refer to stored information. • There is only ONE correct answer for each multiple-choice question. No partial credit will be awarded. • You will be asked to show your University student ID card when you turn in your exam. Discussion section reminder: Section 003 TUE/THUR 08:00-09:00 Salin Bernstein Section 004 TUE/THUR 09:00-10:00 Salin Bernstein Section 005 TUE/THUR 10:00-11:00 Salin Bernstein Section 006 TUE/THUR 12:00-13:00 Salin Bernstein Section 007 TUE/THUR 13:00-14:00 Salin Bernstein Section 008 TUE/THUR 14:00-15:00 Salin Bernstein Section 009 TUE/THUR 14:00-15:00 Konstantin Bobkov Section 010 TUE/THUR 15:00-16:00 Arthur Cole Section 011 TUE/THUR 16:00-17:00 Konstantin Bobkov Section 012 TUE/THUR 12:00-13:00 Andrew Tomasch Section 016 TUE/THUR 11:30-13:00 Arthur Cole Section 017 TUE/THUR 13:00-14:30 Arthur Cole Section 018 TUE/THUR 08:00-09:00 Andrew Tomasch Section 019 TUE/THUR 09:00-10:00 Andrew Tomasch PHYS 125 Fall 2007 Exam 3 11/29/2007 - 2 - Form #1 Moments of inertia for some geometric shapes The acceleration of gravity at the Earth’s surface is 9.8 m/s 2 PHYS 125 Fall 2007 Exam 3 11/29/2007 - 3 - Form #1 1. What is the moment of inertia for the three 2 kg masses arranged in a triangle and rotated about the axis shown in the diagram below? A) 7 kg-m 2 B) 18 kg-m 2 C) 9 kg-m 2 D) 6 kg-m 2 E) 12 kg-m 2 2. A mass on a horizontal frictionless surface is attached to a spring and oscillates with Simple Harmonic Motion. If the amplitude of the oscillation is doubled, what effect does this have on the total mechanical energy? A) It is increased by a factor of 2. B) It is increased by a factor of 2 . C) It is increased by a factor of 4. D) The total mechanical energy does not change. E) It is increased by a factor of 3. PHYS 125 Fall 2007 Exam 3 11/29/2007 - 4 - Form #1 3. The precession of the of a gyroscope in a horizontal circle is a direct illustration of: A) The Impulse-Momentum Theorem formulation of Newton's Second Law for rotational motion. B) The conservation of linear momentum. C) Non-Conservative work for rotational motion. D) The Work-Energy theorem applied to rotational motion. E) The conservation of angular momentum because the gyroscope is an isolated system. 4. A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 3.50 m/s at the bottom of the rise. Find the translational speed at the top. A) 1.1 m/s B) 1.9 m/s C) 1.7 m/s D) 2.3 m/s E) 1.3 m/s PHYS 125 Fall 2007 Exam 3 11/29/2007 - 5 - Form #1 5. The puck in the figure below has a mass of 0.20 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 80.0 cm/s. The string is then pulled downward through the hole in the frictionless table. What is the speed of the puck after the string is pulled downward 15.0 cm? (The puck may be treated as a point mass.) A) 30 cm/s B) 50 cm/s C) 205 cm/s D) 128 cm/s E) 213 cm/s 6. A slab of ice (the density of ice is 920 kg/m 3 ) floats on a freshwater lake (the density of water is 1000 kg/m 3 ). What minimum volume must the slab have for a 45.0-kg black bear cub to be able to stand on it without sinking? A) 0.56 m 3 B) 0.85 m 3 C) 0.68 m 3 D) 0.34 m 3 E) 0.27 m 3 PHYS 125 Fall 2007 Exam 3 11/29/2007 - 6 - Form #1 7. A hollow ring, a solid sphere and a solid cylinder all roll without slipping down an inclined plane. They all have the same radius and are started together with their centers aligned. In what order do they reach the bottom of the slope? A) Sphere, Ring, Cylinder B) Cylinder, Sphere, Ring C) Cylinder, Ring, Sphere D) Ring, Cylinder, Sphere E) Sphere, Cylinder, Ring 8. A figure skater performs her routine while holding a 1.0 kg mass in each hand. For the finale, she goes into a spin with her arms tucked close to her body (moment of inertia I 1 ) rotating at a rate of ω 1 . She extends her arms out changing her moment of inertia to I 2 and her rotation rate to ω 2 . Which of the following statements is true? A) ω 2 <ω 1 because angular momentum is conserved and her moment of inertia increases. B) ω 2 <ω 1 because a net external torque acts and does negative work, reducing her rotational kinetic energy. C) ω 2 >ω 1 because angular momentum is conserved and her moment of inertia decreases. D) ω 2 >ω 1 because a net external torque acts and does positive work, increasing her rotational kinetic energy. E) ω 2 >ω 1 because rotational kinetic energy is conserved. PHYS 125 Fall 2007 Exam 3 11/29/2007 - 7 - Form #1 9. A heavy crate of mass M hangs from a cylindrical steel cable of length L and diameter D as shown below, stretching the cable by a distance d. If a second cable is substituted which has twice the length and twice the diameter of the original cable, the new cable stretches by an amount: A) d B) d/4 C) 2d D) Cannot be determined without the Young's Modulus for steel. E) d/2 10. A simple crane is made from a solid uniform rod, of length L and mass m, hinged at point O. It is used to support a wrecking ball, of mass M, hanging by a chain from the end of the rod. The rod is supported at an angle θ to the horizontal by a horizontal force, of magnitude F, applied to a chain attached to the rod at a point 2/3 of the way along the rod from the hinge. The system is in equilibrium. Ignoring the mass of the chains, find an expression for the magnitude of the force F in terms of m, M, g and θ. A) 3( ) 2cos mM F θ + = B) (2 ) 4cot mMg F θ + = C) tan Mg F m θ = + D) (3 2 ) tan mMg F θ + = E) 3( 2 ) 4tan mMg F θ + = PHYS 125 Fall 2007 Exam 3 11/29/2007 - 8 - Form #1 11. The gauge pressure at a depth of 2.7 meters in mineral oil 3 ( 800 kg/m )ρ = oil is: A) 5.22 x 10 4 Pa B) 2.12 x 10 4 Pa C) 3.51 x 10 4 Pa D) 0.88 x 10 4 Pa E) 1.33 x 10 4 Pa 12. Doctor Who frequently gets lost in the solar system, so he keeps a mass on a string (his yo-yo) which serves as a simple pendulum so that he can always figure out what planet he happens to be on. On Mars, where the acceleration due to gravity is 0.376gg= Mars Earth , the pendulum oscillates with a period of 1.5 s when it is set into small-angle oscillations. During one journey, the good Doctor finds himself on a planet where the pendulum oscillates with a period of 0.92 s. Which planet is he on? A) Jupiter, where 2.358 Jupiter Earth gg= . B) He is not on a planet; he is on the earth's moon where 0.167 Moon Earth gg= . C) Earth, where 2 9.80 m/s Earth g = . D) Venus, where 0.904 Venus Earth gg= . E) Uranus, where 0.886 Uranus Earth = . PHYS 125 Fall 2007 Exam 3 11/29/2007 - 9 - Form #1 13. A block, of mass 2.05 kg, on a frictionless horizontal surface is pushed against a spring with a spring constant of 455 N/m so that the spring is compressed by 20.0 cm. The block is then released from rest and the spring projects the block along the surface and up a frictionless curved incline as shown. Calculate the height h above the horizontal surface that the block reaches before momentarily coming to rest. A) 2.68 m B) 1.35 m C) 0.005 m D) 0.23 m E) 0.45 m 14. A 1993 Nissan 300 ZX 2+2 coupe (1.5 liter displacement, dual overhead cam, 6 cylinder, 24 valves, no turbo charger) develops 212 horsepower (1 horsepower = 746 Watts) with the engine drive shaft rotating at 3500 revolutions/minute. The torque on the drive shaft is closest to: A) 431 N-m B) 276 N-m C) 512 N-m D) 610 N-m E) 312 N-m PHYS 125 Fall 2007 Exam 3 11/29/2007 - 10 - Form #1 15. A mass is attached to the free end of an ideal spring and executes Simple Harmonic Motion (SHM) described by the equation x(t)=0.5 cos(18 t) where x is in meters and t is in seconds. What is the magnitude of the maximum acceleration the mass experiences during SHM? A) 112 m/s 2 B) 124 m/s 2 C) 137 m/s 2 D) 162 m/s 2 E) 97 m/s 2 16. While fishing, you are using a "bobber", a small cylinder of balsa wood (densityρ balsa , cross sectional area A and height H) to suspend your bait below the surface of the water (densityρ 2 HO ). The bobber is floating in equilibrium when a big fish tugs on it and submerges it a distance y further under the surface of the water from its equilibrium position. The fish then gets away (the big ones always do) and you are left to console yourself by calculating the properties of the resulting Simple Harmonic Motion (SHM) of the bobber as it oscillates vertically up-and-down in the water about its original equilibrium position. Ignoring any effects due to the bait hanging from the bobber, the angular frequency for the resulting oscillations is: A) g H ρ ω ρ = 2 HO SHM balsa B) 2 g H ρ ω ρ = 2 HO SHM balsa C) g H ω = SHM D) 2 g H ρ ω ρ = 2 balsa SHM HO E) g H ρ ω ρ = 2 balsa SHM HO PHYS 125 Fall 2007 Exam 3 11/29/2007 - 11 - Form #1 17. A solid cylinder is mounted on a horizontal frictionless axel. Attached to it and wrapped around several times is a light string. A mass m is attached to the free end of the string as shown. The cylinder, with mass M = 0.675 kg and radius r, has moment of inertia 2 1 2 Mr . When the system is released it is found that the hanging mass m has an acceleration of 4.70 m/s 2 . Calculate the mass m. A) 0.219 kg B) More information is needed. C) 0.109 kg D) 0.649 kg E) 0.311 kg 18. A uniform rod of mass M and length L is pivoted at one end (I = 1/3 ML 2 ) to form a pendulum, displaced a small angleθ from the vertical and released. The angular frequency of the resulting oscillations is: A) 1 3 g L B) 3 2 g L C) 1 2 g L D) 1 5 g L E) g L PHYS 125 Fall 2007 Exam 3 11/29/2007 - 12 - Form #1 19. An 8 g bullet is shot into a 4.0 kg block, at rest on a horizontal frictionless surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 5.6 cm. The force constant of the spring is 1900 N/m. The initial velocity of the bullet is closest to: v 1900 N/m 4 kg A) 640 m/s B) 660 m/s C) 610 m/s D) 680 m/s E) 580 m/s 20. A sphere of mass M = 2 kg and radius R = 0.1 m is held in place against a wall by a massless string connected to the wall at an angle θ = 25° from the vertical. The string connects to the sphere tangentially as shown in the figure. What is the magnitude of the frictional force provided by the wall? A) 36.0 N B) 87.5 N C) 17.7 N D) 10.3 N E) 55.5 N atomasch Microsoft Word - physics_125_f07_exam_3_form1_noanswers.doc