Exam 3 Questions - Foundations of Physics I | PHYS 2305, Exams of Physics

Download Exam 3 Questions - Foundations of Physics I | PHYS 2305 and more Exams Physics in PDF only on Docsity! Name: ________________________________________ Date:_____________ Instructor: ________________________________________ Physics 2305 – Spring 2013 Exam 3 Form A This test has twenty-one questions BEFORE YOU BEGIN: 1. Fill in your ID number and the exam form letter on the scantron. 2. Write your name on the exam and the scantron. 3. Check that that you did #1 and #2 correctly. 4. Sign the honor pledge below 5. Do not start working until you are told to. You will find three pages of scratch paper at the end of the exam – there is more up front if you need it. You are allowed to take the exam apart, but if you do, please staple it back together before turning it in. I pledge that I have neither given nor received assistance during this examination, and that I will not discuss the contents of this examination with anyone before end of the exam period. Signed:_______________________________ Constants and conversions: g = 9.8 m/s2 (gravitational acceleration near Earth’s surface) G = 6.67×10-11 N m2/kg2 (gravitational constant) R = 8.31 J/(mol·K) (ideal gas constant) k = 1.38×10-23 J/K (Boltzmann constant) 1 atm = 101 000 Pa (1 Pa = 1 N/m2) 0°C = 273.15 K Radius of Earth: 6.38 x 106 m Mass of Earth: 5.97 x 1024 kg Mathematical Relations: 𝑐𝑐2 = 𝑎𝑎2 + 𝑏𝑏2 − 2𝑎𝑎𝑏𝑏 cos𝜃𝜃 sin(90° − 𝜃𝜃) = cos𝜃𝜃 cos(90° − 𝜃𝜃) = sin𝜃𝜃 sin2 𝜃𝜃 + cos2 𝜃𝜃 = 1 sin 2𝜃𝜃 = 2 sin𝜃𝜃 cos𝜃𝜃 cos 2𝜃𝜃 = cos2 𝜃𝜃 − sin2 𝜃𝜃 For small x: (1 + 𝑥𝑥)𝑛𝑛 ≈ 1 + 𝑛𝑛𝑥𝑥 𝑒𝑒𝑥𝑥 ≈ 1 + 𝑥𝑥 sin𝑥𝑥 ≈ 𝑥𝑥 cos𝑥𝑥 ≈ 1 − 1 2 𝑥𝑥2 tan𝑥𝑥 ≈ 𝑥𝑥 If 𝑎𝑎𝑥𝑥2 + 𝑏𝑏𝑥𝑥2 + 𝑐𝑐 = 0, then 𝑥𝑥 = −𝑏𝑏 ± √𝑏𝑏2 − 4𝑎𝑎𝑐𝑐 2𝑎𝑎 Moments of inertia: 1m 5. A block of mass m1 = 0.5 kg rests on a frictionless table. A string attached to the block passes over a frictionless pulley and is attached to a block of mass m2 = 1 kg. The pulley is a uniform disk of mass m3 = 1 kg and radius 0.15 m. As the mass m2 falls, the string does not slip on the pulley. With what acceleration does the mass m2 fall? A. 5.6 m/s2 B. 4.9 m/s2 C. 2.1 m/s2 D. 9.8 m/s2 E. 0 m/s2 6. A solid sphere of radius 0.1 m and mass 0.5 kg starts at rest at the top of an incline plane and is rolling without slipping. The plane makes an angle of 300 with the horizontal and has a vertical height of 1 m. What is the velocity of the center of mass of the sphere at the time when it reaches the bottom of the incline? A. 6.3 m/s B. 3.7 m/s C. 9.8 m/s D. 4.9 m/s E. 0 m/s E N 36.9 0 7. A 20g ball of clay is travelling east at 2m/s, collides with a 30g ball of clay travelling north at 1m/s. They stick together and move in the direction shown in the figure. What is the speed of the two balls after collision? A. 3.0 m/s B. 2.4 m/s C. 1.0 m/s D. 8.3 m/s E. 9.8 m/s 8. Which of the following is true about the center of mass of a system? A. The total linear momentum of the system is always bigger than the momentum of the center of mass of the system. B. The center of mass of the system accelerates due to the internal forces of the system C. The center of mass of the system never accelerates. D. The rate of change of the momentum of the center of mass is always equal to the net external force. E. None of the above are true 9. A particle of mass 4.0 kg, initially moving along axis X with a velocity of 2.0 m/s collides elastically with a particle of mass 6.0 kg initially moving along axis X with a velocity of -4.0 m/s. What is the velocity of the particle with mass 4.0 kg after the collision? A. 2.0 m/s B. -4.0 m/s C. -5.2 m/s D. 0.8 m/s E. -1.8 m/s 10. A spinning figure skater pulls his arms in as he rotates on the ice. As he pulls his arms in, what happens to his angular momentum L and kinetic energy K? A. L and K both increase. B. L stays the same; K increases. C. L increases; K stays the same. D. L and K both stay the same. E. L and K both decrease. 11. Two uniform spheres are fixed at the positions shown in the figure below. If a particle with mass 0.020 kg is placed at the position P. What is the magnitude of the force on the particle? A. 6.674 × 10-13 N B. 4.719 × 10-13 N C. 2.309 × 10-13 N D. 0 N E. 3.337 × 10-13 N Wood brass 18. A rocket is launched vertically up from the surface of earth’s north pole with velocity 𝑣𝑣0 = 4000 𝑚𝑚/𝑠𝑠. If the air resistance is negligible find the height which the rocket will reach. (𝐸𝐸𝑎𝑎𝐸𝐸𝐸𝐸ℎ′𝑠𝑠 𝐸𝐸𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟𝑠𝑠 𝑟𝑟𝑠𝑠 𝑅𝑅𝐸𝐸 = 6.38 × 106𝑚𝑚) A. 120 km B. 2000 km C. 936 km D. 259 km E. 500 km 19. A 20g bullet moving horizontally at 50m/s, strikes a 7kg block resting on a table. The bullet embeds into the block after the collision. Find the force of friction between the block and the table if the block moves 1.5m before stopping. A. 0.047N B. 0.63N C. 0.32N D. 0.13N E. 0.25N 20. A rod of length L=1m is composed of a uniform length L/2 of wood with mass 𝑚𝑚𝑊𝑊 = 50𝑔𝑔, and a uniform length L/2 of brass with mass 𝑚𝑚𝐵𝐵 = 100𝑔𝑔. Find the moment of inertia of the rod about an axis through the wood end. A. 0.0625 𝑘𝑘𝑔𝑔.𝑚𝑚2 B. 0.0125 𝑘𝑘𝑔𝑔.𝑚𝑚2 C. 0.0350 𝑘𝑘𝑔𝑔.𝑚𝑚2 D. 0.250 𝑘𝑘𝑔𝑔.𝑚𝑚2 E. 0.0550 𝑘𝑘𝑔𝑔.𝑚𝑚2 21. If the sun somehow collapsed to form a black hole with the same mass, what effect would this event have on the orbit of the earth? A. The period and orbital radius will increase B. The period and orbital radius will decrease C. The period and orbital radius remain the same D. The earth will fall onto the black hole E. The earth will overcome the gravitational pull of the black hole and escape the solar system Key A Key B Key C Q 1 D E A Q 2 A C E Q 3 D B A Q 4 B D E Q 5 B A C Q 6 B C D Q 7 C D C Q 8 D C A Q 9 C E D Q 10 B E A Q 11 B A D Q 12 B D A Q 13 D B D Q 14 A C B Q 15 B D A Q 16 A C E Q 17 A E C Q 18 C A D Q 19 A D E Q 20 A E A Q 21 C B C