# Energy on an Incline 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 ball along an incline.

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 Incline 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 ball along a series of hills and allows the user to measure the speed and height of the ball at various locations. From these measurements, the total amount of mechanical energy can be compared at various locations in the ball's path.

### 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 ball as it moves through along the hill and categorize them as being either internal or external forces. (Assume no air resistance)

### External Forces

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

3. Consider the diagram below for a ball which starts at rest at point A and rolls from A to B to C to D to E to F.

Would you expect the mechanical energy of the ball to be conserved as it rolls from the elevated position into the valley and over the smaller hill? ___________ 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 six positions marked in the diagram above.

5. Using complete sentences, describe what happens to the amount (increasing or decreasing) of kinetic energy and the amount of potential energy (increasing or decreasing) as the ball moves from A to B to C to D to E to F. Be clear and specific.

6. If air resistance had a significant influence on the motion of the ball, 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 5 kg, then click on the Reset button and then enter 5 kg into the Mass Input Box. If the Height is not set to 40 meters, then click on the Reset button and then enter 40 m into the Height Input Box. Set the Air Resistance to None.

Click on the Run button to run the simulation. As the simulation runs, observe that the current height and the speed of the ball are displayed in the on-screen meters at the bottom 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 the five positions corresponding approximately to the five positions marked B, C, D, E and F in the diagram above (Note: A is the starting location). Record values of height and speed for the ball and determine the kinetic energy, potential energy and the total mechanical energy at all six locations (includes the rest position A). Be sure to show your work for the three calculations.

Part B: Effect of Mass upon Speed at Points C and E

Reset the simulation to the initial conditions using the Reset button. Then run the simulation and pause it just prior to reaching point C. 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. Allow the simulation to Continue and repeat the measurement o speed at Point E; use the slider controls to step the simulation to the precise point. Reset the simulation by clicking on the Reset button and then modify the Mass of the ball (to any values between 5 kg and 40 kg). Use the same initial ball height of 40 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 10 kg, then the click on the Reset button and then enter 10 kg into the Mass Input Box. Be sure that the Height of Ball is set to 40 m and the Height of Ball is set to 40 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 Point C. 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 ball 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 Ball = ________ kg

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

* 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) Speed at E (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 ball 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 six locations along the ball's path. Then for each individual location, calculate the percent difference between the average TME value and the TME value at that location. PSYW

Average TME value =+ _________________ J

 Location A Location B Location C Location D Location E

3. In Part B of this lab, does the mass of the ball effect the speed of the ball when it reaches location C and location D? _________ 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 10-kg ball starts from rest at a height of 50-meter and slides to a lower point. If the lower point is 15-meter high, determine the speed at this point. PSYW

2. A 30-kg ball starts from rest at a height of 50-meter and slides to a lower point. If the lower point is 15-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 ball seem to effect its final speed? __________ Explain.

6. For a free-falling ball, does the mass of the ball 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 ball when it reaches 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 the ball as it rolls along the path. Be clear and specific. Do a bang-up job.