# Energy of a Pendulum Lab

 Materials: Macintosh Computer and either School Server or Room 159 Computer Lab Time Allotment: 5 Class Days

### Purpose:

The purpose of this activity is to use an Interactive Physics simulation to investigate the conservation of mechanical energy for the motion of a pendulum.

This lab must be done on a Macintosh computer connected to the school network or upon a computer in the Science Computer Lab. To prepare for the lab, do the following steps.

1. Log onto the school network in the usual manner.
2. Open the Interactive Physics application.
3. Choose Open... from the File menu. Navigate to the GBS Simulations folder and open the file titled Pendulum Energy by double-clicking on its name. The simulation window shown below will appear.

An Interactive Physics file will open. The file simulates the motion of a pendulum and allows the user to measure the speed and height of the pendulum bob at various locations. From these measurements, the total amount of mechanical energy can be compared at various locations in the pendulum's trajectory.

### Pre-Lab Analysis:

Prior to the start of the procedure, complete the following pre-lab section. The successful completion of these questions will prepare you for the analysis of your collected data.

1. Identify the forces acting upon the pendulum bob as it moves through its trajectory and categorize them as being either internal or external forces. (Assume no air resistance)

### External Forces

2. Of the external forces acting upon the bob, which (if any) do work upon the bob? Explain your answer.

3. Would you expect the mechanical energy of the pendulum bob to be conserved as it swings from position A to position B to position C? ___________ Explain your answer.

4. Express your expectation by filling in the bar chart below for the kinetic energy (KE), potential energy (PE), and total mechanical energy (TME) at the five positions.

5. Using complete sentences, describe what happens to the amount of kinetic energy and the amount of potential energy as the pendulum bob moves from A to B to C to D to E. Be clear and specific.

6. If air resistance had a significant influence on the motion of the pendulum bob, then how would your answers to questions #2, #3, and #4 be different. Explain using complete sentences.

7. State the two equations used to determine the kinetic and potential energy.

### Procedure:

Part A: Effect of Height upon Mechanical Energy

 Note: If the mass is not set to 1 kg, then click on the Reset button and then enter 1 kg into the Mass Input Box. If the String Length is not set to 2.5 meters, then click on the Reset button and then enter 2.5 m into the String Length Input Box. Set the Air Resistance to None.

Set the initial pendulum Height of Bob to 2.0 meters and click on the Run button to run the simulation. As the simulation runs, observe that the current height and the speed of the pendulum are displayed in the on-screen meters on the right side of the window. The simulation can be paused by clicking on the Stop button and continued by clicking on the Continue button. Pause the simulation at five positions corresponding approximately to the five positions marked A, B, C, D and E in the diagram above. Record values of height and speed for the pendulum bob and determine the kinetic energy, potential energy and the total mechanical energy at each of the five locations. Be sure to show your work for the three calculations.

Part B: Effect of Mass upon Speed at Point C

Reset the simulation to the initial conditions using the Reset button. Then run the simulation and pause it just prior to reaching the lowest point. If necessary drag the slider in the bottom of the simulation window (or merely click on the step forward and step backward buttons as depicted in the graphic at the right) until the simulation steps through to the desired point - Point C. Observe and record the speed at this point. Reset the simulation by clicking on the Reset button and then modify the Mass of the pendulum bob (to any values between 1 kg and 5 kg). Use the same initial pendulum bob height of 2.0 meters in each trial. Repeat the simulation and record data in the Part B Data Table below. Important: Be sure to Reset the simulation prior to modification of the mass.

Part C: Effect of Air Resistance upon Mechanical Energy

 Note: If the mass is not set to 1 kg, then the click on the Reset button and then enter 1 kg into the Mass Input Box. Be sure that the Initial Height of Bob is set to 2.0 m and the String Length is set to 2.5 m. Set the Air Resistance to None.

Now rerun the simulations with varying amount of air resistance and pause it just prior to reaching the lowest point. If necessary drag the slider in the bottom of the simulation window (or merely click on the step forward and step backward buttons) until the simulation steps through to the desired point - Point C. Observe and record the speed at this point. Reset the simulation by clicking on the Reset button and then modify the Air Resistance acting upon the pendulum bob by using the Air Resistance button. Repeat the simulation and record data in the Part C Data Table below. Important: Be sure to Reset the simulation prior to modification of the air resistance.

### Data:

Part A: Effect of Height upon Mechanical Energy

Mass of Pendulum Bob = ________ kg

 Location Height (m) Speed (m/s) PE (J) * KE (J) * TME (J) * A ________ ________ ________ ________ ________ B ________ ________ ________ ________ ________ C ________ ________ ________ ________ ________ D ________ ________ ________ ________ ________ E ________ ________ ________ ________ ________

* indicates please show your work in the cells of the Data Table

Part B: Effect of Mass upon Speed at Point C

 Trial Mass (kg) Speed at C (m/s) 1 ________ ________ 2 ________ ________ 3 ________ ________ 4 ________ ________ 5 ________ ________

Part C: Effect of Air Resistance upon Mechanical Energy

 Trial Air Resistance Speed at C (m/s) 1 k = 0 kg/m*s ________ 2 k = 2 kg/m*s ________ 3 k = 4 kg/m*s ________ 4 k = 6 kg/m*s ________ 5 k = 8 kg/m*s ________ 6 k = 10 kg/m*s ________

### Post-Lab Analysis and Questions:

1. Based on your data in Part A of this lab, is the mechanical energy of the pendulum bob conserved? Support your answer by using actual data from the table in the Data section.

2. In Part A, determine the average value for the total mechanical energy (TME) for all five locations along its trajectory. Then for each individual location, calculate the percent difference between the average TME value and the TME value at that location. PSYW

 Location A Location B Location C Location D Location E

3. In Part B of this lab, does the mass of the pendulum bob effect the speed of the bob when it reaches the lowest location in its trajectory (point C)? _________ Support your answer by using actual data from the table in the Data section.

4. Use the work-energy theorem to solve the following two problems.

KEi + PEi +Wext = KEf + PEf

1. A 1-kg pendulum bob starts from rest at a height of 1-meter and swings to its lowest point. If the lowest point is 0.25-meter high, determine the speed at this point. PSYW

2. A 3-kg pendulum bob starts from rest at a height of 1-meter and swings to its lowest point. If the lowest point is 0.25-meter high, determine the speed at this point. PSYW

5. Based on the answers to the questions in #4 above, does the mass of the object seem to effect its final speed? __________ Explain.

6. For a free-falling object, does the mass of the object effect the rate of acceleration and the final speed after a given period of motion? __________ Explain.

7. In Part C of this lab, what effect (if any) does the presence of air resistance have upon the total mechanical energy and the speed of the bob when it reaches the lowest location in its trajectory (point C)? _________ Support your answer by using actual data from the table in the Data section.

8. Explain your observation in #7 above by using the work-energy theorem.

### Conclusion:

Discuss what is meant by total mechanical energy and explain what happens to the total mechanical energy and the individual forms (potential and kinetic) of mechanical energy for a pendulum bob as it swings back and forth. Be clear and specific. Do a bang-up job.