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Oscillatory motion (non-constant acceleration)

6.3.1. An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true? a) The work done by the tension force is zero joules.

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Oscillatory motion (non-constant acceleration)

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  1. 6.3.1. An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true? a) The work done by the tension force is zero joules. b) The net work done by the two forces is zero joules. c) The work done by the gravitational force is zero joules. d) The magnitude of the work done by the gravitational force is larger than that done by the tension force. e) The magnitude of the work done by the tension force is larger than that done by the gravitational force.

  2. 6.3.5. Consider the box in the drawing. We can slide the box up the frictionless incline from point A and to point C or we can slide it along the frictionless horizontal surface from point A to point B and then lift it to point C. How does the work done on the box along path A-C,WAC, compare to the work done on the box along the two step path A-B-C, WABC? a) WABC is much greater than WAC. b) WABC is slightly greater than WAC. c) WABC is much less than WAC. d) WABC is slight less than WAC. e) The work done in both cases is the same.

  3. 6.5.1. Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice the mass of the other. When the balls reach the ground, how do the kinetic energies of the two balls compare? a) The lighter one has one fourth as much kinetic energy as the other does. b) The lighter one has one half as much kinetic energy as the other does. c) The lighter one has the same kinetic energy as the other does. d) The lighter one has twice as much kinetic energy as the other does. e) The lighter one has four times as much kinetic energy as the other does.

  4. 5.2.1. A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. By which one of the following means can the centripetal acceleration of the ball be increased by a factor of two? a) Keep the radius fixed and increase the period by a factor of two. b) Keep the radius fixed and decrease the period by a factor of two. c) Keep the speed fixed and increase the radius by a factor of two. d) Keep the speed fixed and decrease the radius by a factor of two. e) Keep the radius fixed and increase the speed by a factor of two.

  5. 5.3.3. A ball is attached to a string and whirled in a horizontal circle. The ball is moving in uniform circular motion when the string separates from the ball (the knot wasn’t very tight). Which one of the following statements best describes the subsequent motion of the ball? a) The ball immediately flies in the direction radially outward from the center of the circular path the ball had been following. b) The ball continues to follow the circular path for a short time, but then it gradually falls away. c) The ball gradually curves away from the circular path it had been following. d) The ball immediately follows a linear path away from, but not tangent to the circular path it had been following. e) The ball immediately follows a line that is tangent to the circular path the ball had been following

  6. 5.3.5. Imagine you are swinging a bucket by the handle around in a circle that is nearly level with the ground (a horizontal circle). What is the force, the physical force, holding the bucket in a circular path? a) the centripetal force b) the centrifugal force c) your hand on the handle d) gravitational force e) None of the above are correct.

  7. Oscillatory motion (non-constant acceleration) Simple Harmonic Motion

  8. 10.1 The Ideal Spring and Simple Harmonic Motion spring constant Units: N/m

  9. 10.1 The Ideal Spring and Simple Harmonic Motion HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRING The restoring force on an ideal spring is

  10. 10.2 Simple Harmonic Motion and the Reference Circle file:///Users/silvinagatica/Desktop/simulations/applets/sim08.htm amplitude A: the maximum displacement period T: the time required to complete one cycle frequency f: the number of cycles per second (measured in Hz)

  11. 10.2 Simple Harmonic Motion and the Reference Circle DISPLACEMENT VELOCITY ACCELERATION

  12. 10.2 Simple Harmonic Motion and the Reference Circle FREQUENCY OF VIBRATION

  13. 10.2 Simple Harmonic Motion and the Reference Circle Example 6 A Body Mass Measurement Device The device consists of a spring-mounted chair in which the astronaut sits. The spring has a spring constant of 606 N/m and the mass of the chair is 12.0 kg. The measured period is 2.41 s. Find the mass of the astronaut.

  14. 10.2 Simple Harmonic Motion and the Reference Circle

  15. 10.3 Energy and Simple Harmonic Motion F=-kx F Work=Area = xf x x0 -kx0 -kxf

  16. 10.3 Energy and Simple Harmonic Motion DEFINITION OF ELASTIC POTENTIAL ENERGY The elastic potential energy is the energy that a spring has by virtue of being stretched or compressed. For an ideal spring, the elastic potential energy is SI Unit of Elastic Potential Energy:joule (J)

  17. 10.3 Energy and Simple Harmonic Motion simulation

  18. 10.2 Simple Harmonic Motion and the Reference Circle SUMMARY: Period T: time when ωt = 2 π Frequency f: # cycles per second ω: angular frequency (how fast it ocillates) simulation horizontal oscilator

  19. 10.4 The Pendulum A simple pendulum consists of a particle attached to a frictionless pivot by a cable of negligible mass. Does T depend on the mass? simulation

  20. 10.4 The Pendulum A simple pendulum consists of a particle attached to a frictionless pivot by a cable of negligible mass. How much would you change L to double T? simulation

  21. 10.4 The Pendulum Example 10 Keeping Time Determine the length of a simple pendulum that will swing back and forth in simple harmonic motion with a period of 1.00 s.

  22. 10.1 The Ideal Spring and Simple Harmonic Motion Example 1 A Tire Pressure Gauge The spring constant of the spring is 320 N/m and the bar indicator extends 2.0 cm. What force does the air in the tire apply to the spring?

  23. 10.1 The Ideal Spring and Simple Harmonic Motion

  24. 10.5 Damped Harmonic Motion In simple harmonic motion, an object oscillated with a constant amplitude. In reality, friction or some other energy dissipating mechanism is always present and the amplitude decreases as time passes. This is referred to as damped harmonic motion.

  25. 10.5 Damped Harmonic Motion • simple harmonic motion • 2&3) underdamped • critically damped • 5) overdamped

  26. 10.6 Driven Harmonic Motion and Resonance When a force is applied to an oscillating system at all times, the result is driven harmonic motion. Here, the driving force has the same frequency as the spring system and always points in the direction of the object’s velocity.

  27. 10.6 Driven Harmonic Motion and Resonance RESONANCE Resonance is the condition in which a time-dependent force can transmit large amounts of energy to an oscillating object, leading to a large amplitude motion. Resonance occurs when the frequency of the force matches a natural frequency at which the object will oscillate.

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