PHY 211
Laboratory # 7: Energy Analysis for A Pendulum Motion
A gravitational pendulum is an object suspended from a string that is free to move in a vertical plane. The equilibrium position for a pendulum is when the string is vertical. If the pendulum is removed from its equilibrium position, it will have a back and forth motion (oscillations) as the gravity acts as a restoring force. During this lab, we will analyze the kinetic and potential energy of the pendulum.
Objectives:
· to study the equation of the motion for a gravitational pendulum
· to study the energy for a gravitational pendulum
· to study the conservation of energy for a conservative system.
Materials
· Nikon 200CoolPix camera
· Meter stick
· Digital scale.
· Spring
· LoggerPro software
· Masses
You will record the motion of a pendulum and use LoggerPro software to analyze the motion.
Preliminary Questions:
1. After the pendulum is removed from its equilibrium position and released, it will move toward the equilibrium position. What are the forces acting on the pendulum? Draw a free body diagram.
2. Are the forces acting on the pendulum conservative? Explain why or why not for each force.
3. If the air resistance is very small and can be neglected, can we consider the pendulum to be a conservative system? Why or why not?
4. What type(s) of energy does the pendulum have at the release point? When passing through the equilibrium position?
5. When the pendulum passes through the equilibrium position, the net force acting on it is zero. Why doesn’t the pendulum stop at that point?
Procedure:
1. Using a 500 g mass, a lab stand and string set up a pendulum. The length of the pendulum should be at least 1m. Clamp the stand to your table using a C clamp and make sure your set up is stable.
2. Place a meterstick next to the pendulum. The meterstick will be used to scale the movie. Set the camera on the tripod.
3. Start the pendulum by rising the object until the string is horizontal .Using the digital camera, record several cycles of the periodic motion. Review the movie to make sure that the pendulum and the meterstick are visible in each frame. Repeat as necessary until your movie is satisfactory.
4. Turn the camera off. Connect it to the USB port of the computer and turn it on. The “ New Hardware Found” message will pop up. Wait until the message “ New hardware installed and ready to use” is displayed, and then close the message window.
5. From “My Computer”, open F:/Nikon/DCIM/100Nikon. Click and drag to move your movie on the desktop.
6. After the movie is copied on the desktop, double click on the right-bottom corner “Safely remove hardware”. Follow the prompts to disconnect the camera.
Part II Analyzing the movie
1. Open Programs/Vernier Software/LoggerPro 3.3. Close the “Tip of the day” and then select Insert/Movie. Open your movie from the desktop
2. Using the ► icon at the bottom of the screen, play the movie. Using the ▀ icon, stop the movie at the point where you could start collecting data.
3. Click on the right-bottom icon to view a vertical toolbar. To scale the movie, click on the icon from the vertical toolbar. Click and drag from one end to the other of the meter stick.. In the pop-up window, enter the length of the object, 1m
4. Click on the icon to change the origin. Click on the equilibrium position of the object to place the origin at that point. The origin and the 2 coordinates axes will become visible.
5. Select your pointer by clicking on the icon. Click on the500g object.. The movie will advance by one frame. Continue to click on the object until the end of the movie.
6. Deselect the pointer and minimize the movie window .
7. Click on the vertical (y) axis of the graph and select the x position. The graph of the x position for the pendulum will be displayed. What is the shape of the graph? Apply the appropriate type of fit and print your graph.
8. Using the Examine tool, record the moments when the pendulum has the maximum elongation
9. Click on the vertical (y) axis label of the graph and select the x velocity. The graph of the x velocity for the pendulum will be displayed. What is the shape of the graph?
10. Using the Examine tool, find the instantaneous velocity at the moments when the elongation is maximum ( recorded on step 11 above). Write a conclusion
11. LoggerPro can calculate for you the kinetic and the potential energy of the pendulum. From Data, select “ New Calculated Column”. In the pop-up window, enter the name (Kinetic Energy) , the short name (KE) and the units (Jouls). To define the new column, (KE=1/2*m*v2) enter in the Definition box the formula: 0.25*”x velocity”^2 (In this equation, 0.25 represents half of the mass; mass is 500g=0.5 kg)
12. Click on the y axis and select KE. What is the shape of the graph? When is the KE minimum, and when is it maximum?
13. LoggerPro can calculate for you the potential energy of the pendulum. From Data, select “ New Calculated Column”. In the pop-up window, enter the name (Potential Energy) , the short name (PE) and the units (Jouls). To define the new column, (PE=m*g*h) enter in the Definition box the formula: 0.5*9.8*”y position “
14. Click on the y axis and select PE. What is the shape of the graph? When is the PE minimum, and when is it maximum? Where is the zero level for the gravitational potential energy?
15. Using Data/ New calculated Column, calculate and graph the total energy of the pendulum vs. time
16. Describe the graph and find the best fit equation. Explain the significance of the fit parameters (including units)
17. Write a conclusion regarding the relationship between kinetic and potential energy for a pendulum.