Lab Assignment: Conservation of Mechanical Energy ...



Lab Assignment: Conservation of Mechanical Energy Laboratory: Introduction

20 points

This lab will demonstrate the principles behind the law of conservation of mechanical energy. Mechanical energy is never created nor destroyed, but it can be converted from one form to another. In this lab, you will study what happens when mechanical energy is converted between elastic potential energy and gravitational potential energy using a mass on a spring.

First, design an experiment you could construct that might measure elastic potential energy and gravitational potential energy.

• What materials would you use?

• What would you measure?

• What results would you expect?

• What if the results were different; what would that indicate?

o Students choice

Write down your answers; you will include a description of your lab and the answers to these questions as part of your lab write-up that you submit to your teacher.

Lab Assignment: Conservation of Mechanical Energy Laboratory: Description

Developing a Hypothesis:

A mass on a spring will oscillate vertically when it is lifted and released. The gravitational potential energy increases from a minimum at the lowest point to a maximum at the highest point. The elastic potential energy in the spring increases from a minimum at the highest point to a maximum at the lowest point, where the spring is stretched. Because the mass is temporarily at rest, the kinetic energy of the mass is zero at the highest and lowest points. The total mechanical energy at those points is the sum of the elastic and gravitational potential energies.

In this lab, you will use a virtual Hooke’s law apparatus, which combines a stand for mounting a hanging spring and a vertical ruler for measuring the displacement of a mass attached to the spring.

Create hypotheses of what you think the results of this experiment will be.

• How will the elastic potential energy and the gravitational potential energy change at different points in the oscillation?

o Elastic

▪ Bottom will have the greatest

o Potential

▪ Top will have the greatest

• How will the mechanical energy change at different points in the oscillation?

o It will stay constant as long as no energy is lost as other energy such as friction or sound

Defend your hypotheses with your knowledge of the law of conservation of mechanical energy. Your answers will be a part of your lab write-up that you submit to your teacher.

Objectives:

1. Determine the spring constant of a spring.

2. Calculate elastic potential energy.

3. Calculate gravitational potential energy.

4. Evaluate whether mechanical energy is conserved in an oscillating spring.

To view the items that need to be included in your lab write-up along with a grading rubric, please refer to the Guidelines for the Laboratory section.

1. Read the entire lab procedure and plan the steps you will take. 

2. The virtual lab can be found at . Click on the lab called Masses and Springs under Work, Energy, and Power tab.

3. Prepare a data table. Label columns: Trial, Mass (kg), Stretched Spring (m), Force (N), Highest Point (m), and Lowest Point (m). In the first column, number trials 1, 2, and 3. 

|Trial |Mass |Stretched Spring |Force |Highest Point |Lowest point |Initial distance |

|1 |0.05 kg |0.05 m |0.49 N |0 m |0.06 m |0.58 m |

|2 |0.100 kg |0.09 m |0.98 N |0 m |0.16 m |0.58 m |

|3 |0.250 kg |0.250 m |2.45 N |0 m |0.46 m |0.58 m |

Data will vary due to settings

4. Measure the initial location of the spring relative to the ground. Using the ruler on the left side of the screen, measure the distance from the dotted line to the ground represented by the bottom of the screen. Notice that you can click and drag on the ruler to move it around. Record this measurement as Initial Distance (m) in your spreadsheet near your data table. 

5. Pick up the 50 g mass by clicking on it. Hang it on one of the springs. Measure the distance from the dotted line to the bottom of the spring. Record your measurement in the column Stretched Spring in your data table. Also record the mass of the weight in kg. Repeat using masses of 100 g and 250 g. 

6. Now replace the mass with the 50 g mass again. With the mass on the spring, raise it up to the dotted line where the spring rests without a mass on it. Release the mass. Watch the spring closely to identify the high and low points of the oscillation. Notice that you can slow down the oscillation, and pause it using radio buttons on the right side of the screen. Record the values as Highest Point and Lowest Point on your data table. Repeat using the 100 g and 250 g masses.

7. Organizing Data: For each trial in the first table, convert the masses used to their force equivalents. Use the equation Fg = mag.

8. Organizing Data: For each trial in the first table, calculate the spring constant using the equation [pic]. Take the average of all trials, and use this value as the spring constant.

|Trial |Force (N) |Stretched Spring distance m |Spring constant k N/m |

|Trial 1 |0.49 |0.05 |9.8 |

|Trial 2 |0.98 |0.09 |10.88 |

|Trial 3 |2.45 |0.24 |10.2 |

Average: will vary with initial data 10.3 N/m

9. Organizing Data: For each trial in your second data table, calculate the elastic potential energy at the highest point in the trial. Use the equation [pic], where x is the value of the highest point of the oscillation. 

|Trial |Spring constant k |Top distance m |Elastic PE Joules |

|Trial 1 |10.3 |0 |0 |

|Trial 2 |0.98 |0 |0 |

|Trial 3 |2.45 |0 |0 |

10. Organizing Data: For each trial in your second data table, calculate the elastic potential energy at the lowest point in the trial. Use the equation [pic], where x is the value of the lowest point of the oscillation. 

|Trial |Spring constant k |Bottom distance m |Elastic PE Joules |

| |N/m | | |

|Trial 1 |10.3 |0.06 |0.185 |

|Trial 2 |10.3 |0.16 |0.138 |

|Trial 3 |10.3 |0.46 |1.09 |

11. Analyzing Results: Based on your calculations for items 3 and 4, where is the elastic potential greatest? Where is it least? Explain these results in terms of energy stored in the spring. 

1. Greatest at the bottom

2. lowest at the top

1. The stored energy is when it is stretched the most

12. Organizing Data: Calculate the height of the mass at the highest point of each trial. Use the equation Highest = Initial Distance – Highest Point. 

|Trial |Total distance |Top distance m |Spring distance |

| |from ground m | |from ground m |

|Trial 1 |0.58 |0 |0.58 |

|Trial 2 |0.58 |0 |0.58 |

|Trial 3 |0.58 |0 |0.58 |

13. Organizing Data: Calculate the height of the mass at the highest point of each trial. Use the equation Lowest = Initial Distance – Lowest Point. 

|Trial |Total distance to |Bottom distance m |Spring distance |

| |ground m | |from ground |

|Trial 1 |0.58 |0.06 |0.52 |

|Trial 2 |0.58 |0.16 |0.42 |

|Trial 3 |0.58 |0.46 |0.12 |

14. Organizing Data: For each trial, calculate the gravitational potential energy, PEg = magh, at the highest point in the oscillation. 

|Trial |Force N |Top distance from |Gravitational PE |

| | |ground | |

|Trial 1 |0.49 |0.58 |0.284 |

|Trial 2 |0.98 |0.58 |0.412 |

|Trial 3 |2.45 |0.58 |1.421 |

15. Organizing Data: For each trial, calculate the gravitational potential energy at the lowest point in the oscillation. 

|Trial |Force N |Bottom distance |Gravitational PE Joules|

| | |from ground m | |

|Trial 1 |0.49 |0.52 |0.255 |

|Trial 2 |0.98 |0.42 |0.412 |

|Trial 3 |2.45 |0.12 |0.294 |

16. Analyzing Results: According to your calculations in items 8 and 9, where is the gravitational potential energy the greatest? Where is it least? Explain these results in terms of gravity and the height of the mass and the spring. 

1. Greatest at the top

2. lowest at the bottom

1. The stored energy is greatest when the weight is furthest from the ground

17. Organizing Data: Find the total potential energy at the top of the oscillation and at the bottom of the oscillation.

|Trial |Total at bottom |Total at top |

|1 |0.284 |0.0185 + 0.255 = 0.273 |

|2 |0.568 |0.138 + 0.412 = 0.550 |

|3 |1.421 |1.09 + 0.294 = 1.38 |

1. Drawing Conclusions: Based on your data, is mechanical energy conserved in the oscillating mass on the spring? Explain how your data support your answers. How did your results compare to your hypothesis?

1. If there is a difference between the total elastic and total potential energies then it is not conserved, if they are the same it is conserved, the values are close so it can be said the mechanical energy was conserved

2. Making Predictions: How would using a stiffer spring affect the value for the spring constant? How would this change affect the values for the elastic and gravitational potential energies?

1. Increasing the stiffness will increase the spring constant, because it will have as smaller change in distance,

2. Elastic will decrease and gravitational will increase

1. Elastic will decrease because of the smaller distance due to a stiffer spring

2. Total potential will increase because it will be higher from the ground

(Note that you can try this experiment in the virtual lab by changing the stiffness of the spring using the slider on the right side of the screen.)

3. Making Predictions: How would performing this experiment on the moon, where the acceleration due to gravity is only 1/6 of that on Earth affect the values for the elastic and gravitational potential energies?

1. Some effect on the elastic due to forces decreasing

2. Will decrease for gravitational because the force is also decreased

(Note that you can try this experiment in the virtual lab by changing the gravity using the radio buttons on the right side of the screen.)

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