8. What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m string?

Transcription

1 1. In the produce section of a supermarket, five pears are placed on a spring scale. The placement of the pears stretches the spring and causes the dial to move from zero to a reading of 2.0 kg. If the spring constant is 450 N/m, what is the displacement of the spring due to the weight of the pears? 2. When a force of 19 N is applied to a spring, it elongates m. Determine the period of oscillation of a 4.0-kg object suspended from this spring. 3. The displacement of a certain simple harmonic oscillator is given by x = (5 m) cos [(4.0 rad/s) t]. What is the amplitude and period of the simple harmonic motion?

2 4. A ball hung from a vertical spring oscillates in simple harmonic motion with an angular frequency ( of 2.6 rad/s and an amplitude of m. What is the maximum acceleration of the ball? 5. A 2.2-kg object is suspended from a spring with k = 18 N/m. The mass is pulled 0.35 m downward from its equilibrium position and allowed to oscillate. What is the maximum kinetic energy of the object? 6. A 0.2-kg block is held in place by a force F that results in a 0.30-m compression of a spring beneath the block. The spring constant is N/m. Assuming the mass of the spring is negligible compared to that of the block, to what maximum height would the block rise if the force F were removed.

3 7. The spring constant for the spring in a special cannon is 1800 N/m. In cocking the cannon, the spring is compressed 0.55 m. What is the initial speed of a 7.0-kg cannonball at rest on the free end of the spring when it is released? 8. What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m string? 9. A mass vibrates back and forth from the free end of an ideal spring of spring constant 20 N/m with an amplitude of 0.30 m. What is the kinetic energy of this vibrating mass when it is 0.30 m from its equilibrium position?

4 10. Complete the following sentence: Resonance occurs in harmonic motion when A) the system is overdamped. B) the system is critically damped. C) the energy in the system is a minimum. D) the driving frequency is the same as the natural frequency of the system. 11. A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion with amplitude 4.0 cm. What is the energy of the system now? 12. A simple pendulum consists of a 0.25-kg spherical mass attached to a massless string. When the mass is displaced slightly from its equilibrium position and released, the pendulum swings back and forth with a frequency of 2.0 Hz. What frequency would have resulted if a 0.50-kg mass (same diameter sphere) had been attached to the string instead?

5 13. A mass is attached to a spring. It oscillates at a frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is the maximum velocity attained by the mass? 14. Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating? A) critically damped B) underdamped C) slightly damped D) overdamped 15. What is the spring constant of a spring that stretches 2.00 cm when a mass of kg is suspended from it?

6 16. When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of m to m. The same block is attached to the same spring and placed on a horizontal, frictionless surface as shown. The block is then pulled so that the spring stretches to a total length of 0.25 m. The block is released at time t = 0 s and undergoes simple harmonic motion. What is the frequency of the motion? 17. A simple pendulum is made from a 0.75-m-long string and a small 0.50kg ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, what is the period of the pendulum and how much time elapses before it first attains its greatest speed?

7 18. A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, its instantaneous velocity A) is maximum. B) is less than maximum, but not zero. C) is zero. D) cannot be determined from the information given. 19. Two masses, A and B, are attached to different springs. Mass A vibrates with amplitude of 8.0 cm at a frequency of 10 Hz and mass B vibrates with amplitude of 5.0 cm at a frequency of 16 Hz. How does the maximum speed of A compare to the maximum speed of B? A) Mass A has the greater maximum speed. B) Mass B has the greater maximum speed. C) They are equal. D) There is not enough information to determine. 20. A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum? A) at either A or B B) midway between A and B C) one-fourth of the way between A and B D) none of the above 21. The time for one cycle of a periodic process is called the 22. For a periodic process, the number of cycles per unit time is called the 23. For vibrational motion, the maximum displacement from the equilibrium point is called the

8 24. A 2.2-kg object is suspended from a spring with k = 18 N/m. The mass is pulled 0.35 m downward from its equilibrium position and allowed to oscillate. What is the maximum kinetic energy of the object? 25. Using the figure below classify each curve as either an underdamped situation, an overdamped situation, a moderately damped situation, or critical damping.

9 26. A spring with constant k = 78 N/m is at the base of a frictionless, inclined plane. A 0.50-kg block is pressed against the spring, compressing it 0.20 m from its equilibrium position. The block is then released. If the block is not attached to the spring, how far up the incline will it travel before it stops? 27. The position of a simple harmonic oscillator is given by xt ( ) (0.50m)cos t 3 in seconds. What is the maximum velocity and the period of this oscillator? where t is