Pendulum Motion Purpose: To analyze the back-and-forth motion of a pendulum. Getting Ready: Navigate to the Pendulum Motion Simulation found in the Waves and Sound unit of the Physics lnteractives section at The Physics Classroom. (NOTE: this simulation can also be found in the Circular and Satellite Motion unit.) httpswww.physicsclassroom.comr'Physics-|nteractivesWaves-and-Sounda'Pendulum-Motion-Si mulationi Getting AcquaintedIPlay: This interactive consists of a simulation on the left side of the screen and a series of controls on the right side of the screen. The controls include radio buttons and sliders. By default, the simulation opens showing a ball hanging from the end of a light string and swinging along a circular arc. The radio button labeled Ball on a vertical light string is selected. There are three other options to explore. In this lab we will focus on the default option the back-and-forth motion of the ball on a string, aka, a pendulum. The buttons below the simulation allow you to play, pause, reset, and view in slow motion. Observe the radio buttons that control the various displays (top). Experiment with the various display options, turning each on and off by tapping on the buttons and observing what they do. Finally. the sliders at the bottom right side of the screen are motion parameters that can be changed. Experiment with each parameter by dragging their sliders left and right and observing their effect upon the simulated motion. We will be studying these cause-and-effect relationships later in this activity. Part 1: Force Analysis 1. Reset the animation. Make sure you have selected the Ball on a vertical light string. Enable the Show force of gravity and the Show tension options. Disable all other options. The forces acting on the pendulum are shown on the ball and will change direction and size as the ball swings back and forth. We will analyze these forces and look for patterns. Using the sliders: 0 set the Radius to 0.70 m 0 set the Mass to 3.0 kg 0 set the Initial ball height to 0.25 m. 0 set the other values to whatever you wish. 2. Tap Start and observe the forces acting upon the pendulum bob (ball). Does the magnitude andior the direction of the force of gravity change during the motion? 3. Does the magnitude andfor the direction of the tension force change during the motion? % 4. Use a short sentence to describe the direction of these two forces. 5. Consider the following five positions along the trajectory. Draw a free-body diagram for each of the positions. Label the forces according to type. Size your arrows to indicate the relative strength of the forces at each position. Position A Position B Position 0 Position D Position E 6. At what labeled position is the tension force a. The greatest? B. the smallest? 7. Now enable the Show components by tapping on the corresponding radio button. Note that the gravity force is resolved into two components one tangent to the circular path and one that is directed towards center of the circle (radially). At positions A and E (the extreme positions). how does the size of the radial component of gravity compare to the size of the tension force? At position C, how does the size of the radial component of gravity compare to the size of the tension force? 8. Note that the tangential component of gravity is always directed tangent to the arc back towards position C. This is referred to as a restoring force. All objects undergoing periodic motion must experience a restoring force. At which labeled position(s) is the restoring force the greatest? : 9. Any object moving along a circular path must experience a centripetal force (a net inward force). At which labeled position(s) is this net inward force the greatest? ll Part 2: Position-Velocity-Acceleration 10. Reset the simulation. Keep the Radius at 0.70 m. Increase the Initial ball height to 0.50 m. Tap on the Show motion or energy graphs option. Tap the graph to toggle to the display of position, speed / (velocity), and acceleration. The displays assume a A ,x reference frame where the bottom-most position (C) is O m. A movement to the right of this position is in the + EI' _. D direction. A c movement to the left of this position is in the direction. 0 m 11. Start the simulation and observe the graphs as the pendulum moves back-and-forth. Tap on the Slow motion button if necessary. At what labeled position(s) is the pendulum bob (ball) when the velocity is a maximum + value? At what labeled position(s) is the pendulum bob (ball) when the velocity is a maximum - value? 12. Complete these sentences: As the bob moves from an extreme position (A or E) towards the central position (C), the speed (increases, decreases). As the bob moves from C to A, the velocity becomes (more +, more -, less +, less -). As the bob moves from C to E, the velocity becomes (more +, more -, less +, less -). 13. Observe the Acceleration plot. Use the Slow and Pause buttons as necessary to answer: The acceleration is a maximum + (rightward) value at position The acceleration is a maximum - (leftward) value at position The acceleration is a O misls value at position 14. Referring back to Part 1 of this lab, the acceleration is a maximum when the tangential component of gravity is (greatest, O N). And the acceleration is O misls when the tangential component of gravity is (greatest, 0 N). 15. Consider the velocity-time graph below for two complete back-and-forth cycles. Label each dot on the graph with an A, C, or E based on its position at that point in time. 4. 1' me velocity C: Part 3: Energy Analysis 16. Reset the simulation. Keep the Radius at 0.70 m. Increase the Initial ball height to 0.50 m. Close the Graphs option by tapping the Close button (bottom right). Tap on the Show energy bar chart option. Make observations of the bar heights for KE (kinetic energy), PE (potential energy), and 2E (total mechanical energy). Use the Slow and Pause buttons as necessary. 17. As the pendulum bob swings to and fro, how would you describe the amount of total mechanical energy? E 13. At what labeled position(s) is the kinetic energy the greatest? ll 19. At what labeled position(s) is the potential energy the greatest? 20. Complete the bar charts below for positions A through E A B C D E KE PE 2E KE PE EE KE PE IE KE PE IE KE PE 2E 21. Complete the sentences using , ', and = for increase, decrease, and remains the same. As the pendulum bob moves from and extreme position (A or E) to the central position (C) And as the pendulum bob moves from the central position (C) to an extreme the KE ' the PE and the {E l Waves TRUE or FALSE: Identify the following statements as being either true (T) or false (F). T or F? Waves are created by a vibration. As a wave moves through a medium, the individual particles of the medium move from the source of the wave to another location some distance away. Waves are a means of transporting energy from one location to another without actually displacing matter from one location to another. An ocean wave will transport ocean water from near the middle of the ocean to a location near the shore. As mechanical waves move through a medium, particles of the medium undergo a periodic and repeated vibration about a xed position. 6. Describe how a wave is different than a ulse. 7. Mechanical waves propagate or move through a medium because a. the particles of the medium are able to move along the curved wavelike pathway b. one particle pushes or pulls on the adjacent particle which pushes or pulls on the next particle which c. the initial vibration of the medium causes the medium to assume the wavelike shape and this shape subsequently moves from one location to another. 8. Which of the following categories of waves require a medium in order to transport energy from one location to another? a. mechanical b. electromagnetic What's Wrong With This? Suppose you're watching a science fiction movie and one of the scenes involves a spaceship battle in outer space. Spaceship A launches a successful strike on spaceship B. The scene is presented from the perspective of spaceship A. The occupants of spaceship A view spaceship B blowing up as the result of the successful missile strike. They see the flames of the explosion and shortly thereafter hear the thunderous sound of the explosion. While the scene is definitely exciting, there is a significant fault with it in terms of the physics. What law of physics was violated in the filming of the scene? Explain. 10. The arrows on the diagrams below represent the direction of particle motion. Diagram A Diagram B Diagram A shows a _ - pulse and diagram B shows a _ pulse. a. longitudinal, transverse b. transverse, longitudinal 11. Compare the direction in which particles of the medium vibrate for a longitudinal wave compared to a transverse wave. Reference the diagram in question #10 in your discussion