Name Vibrations 2016 Healy/DiMurro 1. In the diagram below, an ideal pendulum released from point A swings freely through point B. 4. As the pendulum swings freely from A to B as shown in the diagram to the right, the gravitational potential energy of the ball Compared to the pendulum's kinetic energy at A, its potential energy at B is A) half as great B) twice as great C) the same D) four times as great A) decreases B) increases C) remains the same 5. The graph below represents the relationship between the force applied to a spring and the elongation of the spring. 2. A 3.0-kilogram mass is attached to a spring having a spring constant of 30. newtons per meter. The mass is pulled 0.20 meter from the spring's equilibrium position and released. What is the maximum kinetic energy achieved by the mass spring system? A) 2.4 J B) 1.5 J C) 1.2 J D) 0.60 J 3. The unstretched spring in the diagram below has a length of 0.40 meter and spring constant k. A weight is hung from the spring, causing it to stretch to a length of 0.60 meter. What is the spring constant? A) 20 N/m B) 9.8 N/kg C) 0.80 N-m D) 0.050 m/n 6. A 20.-newton weight is attached to a spring, causing it to stretch, as shown in the diagram below. How many joules of elastic potential energy are stored in this stretched spring? A) 0.020 k B) 0.080 k C) 0.18 k D) 2.0 k What is the spring constant of this spring? A) 0.050 N/m B) 0.25 N/m C) 20. N/m D) 40. N/m
7. When a spring is stretched 0.200 meter from its equilibrium position, it possesses a potential energy of 10.0 joules. What is the spring constant for this spring? A) 100. N/m B) 125 N/m C) 250. N/m D) 500. N/m 11. The graph below represents the relationship between the force applied to a spring and spring elongation for four different springs. 8. A spring gains 2.34 joules of elastic potential energy as it is compressed 0.250 meter from its equilibrium position. What is the spring constant of this spring? A) 9.36 N/m B) 18.7 N/m C) 37.4 N/m D) 74.9 N/m 9. The diagram below shows three positions, A, B, and C, in the swing of a pendulum, released from rest at point A. [Neglect friction.] Which statement is true about this swinging pendulum? A) The potential energy at A equals the kinetic energy at C. B) The speed of the pendulum at A equals the speed of the pendulum at B. C) The potential energy at B equals the potential energy at C. D) The potential energy at A equals the kinetic energy at B. Which spring has the greatest spring constant? A) A B) B C) C D) D 12. Base your answer to the following question on the diagram below which represents a simple pendulum with a 2.0-kilogram bob and a length of 10. meters. The pendulum is released from rest at position 1 and swings without friction through position 4. At position 3, its lowest point, the speed of the bob is 6.0 meters per second. 10. What is the spring constant of a spring of negligible mass which gained 8 joules of potential energy as a result of being compressed 0.4 meter? A) 100 N/m B) 50 N/m C) 0.3 N/m D) 40 N/m At which position does the bob have its maximum kinetic energy? A) 1 B) 2 C) 3 D) 4
13. As the pendulum swings from position A to position B as shown in the diagram above, what is the relationship of kinetic energy to potential energy? [Neglect friction.] A) The kinetic energy decrease is more than the potential energy increase. B) The kinetic energy increase is more than the potential energy decrease. C) The kinetic energy decrease is equal to the potential energy increase. D) The kinetic energy increase is equal to the potential energy decrease. 16. When a spring is compressed 2.50 x 10 2 meter from its equilibrium position, the total potential energy stored in the spring is 1.25 x 10 2 joule. Calculate the spring constant of the spring. [Show all work, including the equation and substitution with units.] 17. A 0.65-meter-long pendulum consists of a 1.0-kilogram mass at the end of a string. The pendulum is released from rest at position A, 0.25 meter above its lowest point. The pendulum is timed at five positions, A through E. 14. Spring A has a spring constant of 140 Newtons per meter, and spring B has a spring constant of 280 Newtons per meter. Both springs are stretched the same distance. Compared to the potential energy stored in spring A, the potential energy stored in spring B is A) the same B) twice as great C) half as great D) four times as great Based on the information in the diagram and the data table, determine the period of the pendulum. 15. As a pendulum swings from position A to position B as shown in the diagram, its total mechanical energy (neglecting friction) A) decreases B) increases C) remains the same
18. Base your answer to the following question on the information and diagram below. A block of mass m starts from rest at height h on a frictionless incline. The block slides down the incline across a frictionless level surface and comes to rest by compressing a spring through distance x, as shown in the diagram below. Determine the spring constant, k, in terms of g, h, m, and x. [Show all work including formulas and an algebraic solution for k.]
19. In a laboratory exercise, a student kept the mass and amplitude of swing of a simple pendulum constant. The length of the pendulum was increased and the period of the pendulum was measured. The student recorded the data in the table below. 20. Base your answer to the following question on the information below. A pop-up toy has a mass of 0.020 kilogram and a spring constant of 150 newtons per meter. A force is applied to the toy to compress the spring 0.050 meter. a Label each axis with the appropriate physical quantity and unit. Mark an appropriate scale on each axis. b Plot the data points for period versus pendulum length. c Draw the best-fit line or curve for the data graphed. d Using your graph, determine the period of a pendulum whose length is 0.25 meter. Calculate the potential energy stored in the compressed spring. [Show all work, including the equation and substitution with units.]
Answer Key Vibrastions 2016 1. C 2. D 3. A 4. B 5. A 6. D 7. D 8. D 9. D 10. A 11. A 12. C 13. D 14. B 15. C 16. 20. 17. 1.6 seconds 18. PE = mg h PEs = kx 2 kx 2 = mg h k = 2mg h / x 2 19.