Name: Answer Key PHYSICS 1210-04 Final Exam University of Wyoming 2 May 2012 1. (10 points) A cannonball is fired with a speed of 75 m/s at an angle of 30 above horizontal. It lands at its starting height a horizontal distance D from its starting position. Air resistance against the cannonball is negligible. Which one property of the cannonball is constant throughout its trajectory? a. Its kinetic energy is constant. b. Its gravitational potential energy is constant. c. Its acceleration is constant. magnitude g, downward. d. The rate of change of its speed is constant. e. The power exerted on it is constant. f. Its momentum is constant. g. Its angular momentum is constant. h. Its velocity is constant. i. All of these quantities are constant. 2. (10 points) A block is attached by a rope to a bar that is itself rigidly attached to a frictionless ramp. Determine whether the magnitude of the following forces increases, decreases, or remains the same as the incline angle of the ramp increases from zero to 90. same increases decreases increases decreases a. The force of gravity on the block. b. The component of the force of gravity parallel to the ramp. c. The component of the force of gravity perpendicular to the ramp. d. The tension in the cord. e. The normal force on the block from the ramp. A PHYS 1210 Exam 2 page 1 of 6
3. (10 points) An amusement park ride known as the rotor consists of a circular capsule with sloping walls. Riders lean against the walls, the capsule spins about its axis, and then the floor of the capsule drops, leaving the riders supported only by the walls. Indicate which diagram below is a correct free-body diagram for the rider, and then properly label the forces on that diagram. a. b. c. d. e. f. g. normal friction h. i. weight 4. (10 points) A heavy book is released from rest just atop a relaxed Hooke s law spring. The block compresses the spring as it falls until it momentarily stops. What is the block s acceleration while it is momentarily stopped? a. g upward. b. g downward. c. 2 g upward. d. 2 g downward. e. Zero. Here s the quick way to make sense of this: this is simple harmonic motion, starting at the top extreme position. Acceleration there is g downward, so at the bottom it must be g upward. 5. (10 points) A car traveling in the +x ( ) direction brakes to a stop. The car s center of mass is 0.70 m above the road. As the car brakes, in what direction is the torque about its center of mass resulting from the force of static friction between its tires and the road? a. Zero torque. b. +x ( ) c. x ( ) d. +y ( ) e. y ( ) f. +z ( ) g. z ( ) A PHYS 1210 Exam 2 page 2 of 6
Name: 6. (10 points) A physical pendulum consists of a rigid, extended body whose center of mass swings at a distance L from the axis. How does the pendulum s period of oscillation compare to the period of a simple pendulum with the same length L? a. The physical pendulum s period is shorter. b. The physical pendulum s period is the same. c. The physical pendulum s period is longer. d. It depends on the moment of inertia of the body. The physical pendulum has greater inertia, so it will be slower to accelerate. 7. (10 points) Astronomers recently announced that a planet orbiting the nearby red dwarf star Gliese 667C orbits within the habitable zone in which liquid water may exist at the planet s surface. The planet s mass is 4.5 times the mass of Earth. If the planet has the same density as Earth, will the escape speed from its surface be faster or slower than the escape speed from the surface of Earth? a. The escape speed from the planet is slower than the escape speed from earth. b. The escape speed from the planet is faster than the escape speed from earth. c. The escape speed from the planet is equal to the escape speed from earth. d. It is impossible to determine which has the greater escape speed. Its mass is 4.5 times bigger than Earth s, but its radius isn t. 8. (10 points) A standing sound wave in a pipe has five displacement nodes and five displacement antinodes. How many open ends does the pipe have? a. Zero. b. One. c. Two. 9. A rope that has a constant length density µ hangs from the ceiling of a gymnasium. Shaking the bottom end of the rope sends a transverse pulse up the rope. As the pulse travels upward, a. its speed decreases. b. its speed increases. c. its speed does not change. Length density is constant, but tension is greater at the top than at the bottom. A PHYS 1210 Exam 2 page 3 of 6
10. Two sound waves have the same displacement amplitude of 10 6 m. One has a wavelength of 0.30 m and the other a wavelength of 5.0 m. Which has the greater pressure amplitude? Pressure amplitude is BAk, where a. The 0.30-m wave. A is displacement amplitude and k b. The 5.0-m wave. is wavenumber. c. Both have the same pressure amplitude. d. It is impossible to determine which wave has the greater pressure amplitude. 11. (30 points) An old pipe system runs 50 m through a hill. The pipes running into and out of the hill have a radius of 2.0 cm, but the size of the pipe within the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the inlet and outlet sections at 2.5 m/s. Then they release a dye in the water 30 m upstream of the hill and find that it takes 80 s to reach a point 30 m downstream of the hill. What is the average radius of the pipe within the hill? L 1 L 3 L 2 v 1 = L 1 /t 1 ; v 2 = L 2 /t 2 ; v 3 = L 3 /t 3 Total time t = t 1 + t 2 + t 3 = L 1 /v 1 + L 2 /v 2 + L 3 /v 3 L 1 = L 3 = 30 m L 2 = 50 m v 1 = v 3 = 2.5 m/s r 1 = r 3 = 2.0 cm t = 80 s Continuity condition: A 1 v 1 = A 2 v 2 = A 3 v 3 r 1 2 v 1 = r 2 2 v 2 A PHYS 1210 Exam 2 page 4 of 6
Name: 12. (40 points) A bowling ball of mass 5.0 kg and radius 10.1 cm is released with a translational speed of 3.0 m/s onto a level, flat wooden lane. Initially, the ball does not rotate. The coefficient of kinetic friction between the ball and the lane is 0.20. As the ball slides along the lane, the force of kinetic friction on it slows its translation and causes it to rotate. a. How much time elapses before the ball s rotation catches up with its translation and it rolls without slipping? Translation: v = v 0 + at a = F/m = µmg/m = µg v = v 0 µgt Rotation: = 0 + t = /I = µmgr/(2/5 mr 2 ) = 5µg/2R = 5µgt/2R v 0 = 3.0 m/s 0 = 0 µ = 0.2 Rolling without slipping: v = R v 0 µgt = (5µgt/2R)R = 5µgt/2 v 0 = 5µgt/2 + µgt = 7µgt/2 t = 2v 0 /7µg = (2 3.0 m/s)/(7 0.2 9.8 m/s 2 ) = 0.437 s b. What will be the center-of mass translational velocity of the ball when it stops slipping? v = v 0 µgt = v 0 µg(2v 0 /7µg) = v 0 2v 0 /7 = 5v 0 /7 = 2.14 m/s A PHYS 1210 Exam 2 page 5 of 6
13. (30 points) A flexible wire is stretched between two rigid clamps a distance L apart. The tension in the wire is adjusted so that the speed of the transverse waves in the wire is exactly the same as the speed of sound in the surrounding air. a. A hollow pipe is closed at one end and open at the other. How long must the pipe be for its lowest-frequency resonance to have the same frequency as the lowestfrequency resonance of the wire? L D /2 L = /2 = 2L /4 D = /4 D = 2L/4 D = L/2 b. How long must the pipe be for its next-lowest-frequency resonance to have the same frequency as the next-lowest-frequency resonance of the wire? L D 3 /4 L = D = 3 /4 D = 3L/4 14. (5 points extra credit) What equation is short and sweet, full of hidden delight? kx = ma Hooke on the left, Newton on the right Gives you an equation that s really out of sight. Short and sweet, full of hidden delight. And the spring goes up and down and down, and the spring goes up and down. A PHYS 1210 Exam 2 page 6 of 6