Name ______Class ______Date ______

Activity GS21: Conservation of Energy – PE to KE(Motion Sensor)

Concept / DataStudio / ScienceWorkshop (Mac) / ScienceWorkshop (Win)
Energy / GS21 Conserve Energy.DS / G21 Conserve Energy / G21_ENER.SWS

Equipment Needed

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Qty

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Equipment Needed

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Qty

Motion Sensor (CI-6742) / 1 / Masses / ~2 kg
Balance (SE-8723) / 1 / Meter stick / 1
Block / 1 / Ruler, metric (15 cm) / 1
“C” clamp / 1 / 1.2 m Track System (ME-9429A) / 1
Dynamics Cart (inc. w/ Track) / 1 / Tape / 1 roll

What Do You Think?

How well is energy conserved when the elastic potential energy of a spring is transformed into kinetic energy of a moving cart?

Take time to answer the ‘What Do You Think?’ question(s) in the Lab Report section.

Background

Potential energy is sometimes called stored energy. A compressed spring has stored potential energy called elastic potential energy. Kinetic energy is called the energy of motion. An object in motion has kinetic energy.
The amount of force that a spring can push with depends on how far it is compressed and how strong the spring is (called the spring constant). Likewise, the amount of elastic potential energy (stored energy) a spring has depends on how far it has been compressed and the spring constant. /

A spring that is compressed a distance x from its normal position has an amount of elastic potential energy given by:

where PEelastic stands for “elastic potential energy”, k is the spring constant and x is the distance that the spring is compressed.

The amount of kinetic energy that an object has depends on how much mass it has and how fast it is moving. The formula for kinetic energy is:

where KE stands for “kinetic energy”, m is the mass of the object, and v is the speed of the object.

If energy is conserved, the elastic potential energy in the compressed spring will be completely transformed into kinetic energy when the spring pushes an object of mass m.

SAFETY REMINDER

•Do not let the cart hit the Motion Sensor.

•Follow directions for using the equipment.

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For You To Do

In the Pre-Lab for this activity, measure the spring constant of the plunger spring in a dynamics cart. Put heavy masses on the end of the plunger to force the spring to compress. Measure the amount of distance that the spring compresses. Use DataStudio or ScienceWorkshop to make a Graph of force and position that will give you the value of the spring constant k.

In the Procedure for this activity, use the Motion Sensor to measure the motion of a cart after it is pushed by the plunger spring as the spring de-compresses. Use DataStudio or ScienceWorkshop to record the motion and display the initial velocity and maximum kinetic energy of the cart.

Use your data to compare the measured kinetic energy to the calculated elastic potential energy.

Pre-Lab

Equipment Setup and Data Recording

The dynamics cart has a spring-loaded plunger that can be used to push the cart to get it moving. The plunger has three notches so the plunger spring can be compressed to three different distances. /
When the plunger spring is fully compressed, the end cap is even with the end of the cart. When it is not compressed at all, it goes out about 3 cm. Measure this length exactly and record it as the total plunger length.
1.Put the dynamics on end with the plunger at the top. Place the 30cm metric ruler on the side of the cart. Measure the height of the top of the plunger. Record this as your initial plunger height. /
2.Carefully add masses on top of the plunger starting with 500g then adding 100g each time for 4-5 more trials.. Record the total mass and the amount of stretch (from the initial length) in the Data Table.
•You may need to steady the dynamics cart and the pile of masses to keep them from leaning. /
  • In the Data Table, convert the stretch amounts from centimeters to meters (divide by 100).
  • Convert the mass from grams to kilograms (divide by 1000). Determine the force on the plunger by multiplying the mass in kilograms by 9.80 newtons per kilogram (the strength of gravity at Earth’s surface).
  • Measure the mass of the cart on a digital balance. Record in the data section.

Pre-Lab: Data

Total Plunger Length (cm): ______Mass of Cart (g): ______

Table1 – Finding the Spring Constant

Stretch (cm) / Stretch (m) / Mass (g) / Mass (kg) / Force (N)
0 / 0 / 0 / 0 / 0
500.0
600.0
700.0
800.0
900.0

Pre-Lab: Analyze the Data

  1. Open the file titled ‘GS21 Conserve Energy.DS’ (be sure to “save target as” to your server space). You should see a data table (where you will enter spring data), a graph of force vs. stretch, a graph of speed vs. time (you will use this to measure the speed of the cart), and a calculation of KE (this is just a check of your calculations).
  2. Enter the data for FORCE (in Newtons) and STRETCH (in meters) in the data table provided. Use the arrow keys to navigate through the table. As you enter the data, the graph on the left will change.
  3. In the Graph display, observe the slope of the ‘Linear Fit’ of the data. (Note: the graph should be fairly linear if you did this part correctly). The slope of the Force vs. Stretch plot is the spring constantof your spring(in N/m).
  4. Record the value of the slope as the spring constant, k.in the data section.

Procedure

  • Remember, use the Motion Sensor to measure the motion of a cart just after it is pushed by the plunger spring as the spring de-compresses. Use DataStudio to record and display the motion of the cart. You will compare the measured kinetic energy to the calculated elastic potential energy.
    PART I: Computer Setup
  • Connect the Motion Sensor stereo phone plugs to Digital Channels 1 and 2 on the ScienceWorkshop interface. Put the yellow-banded phone plug into Digital Channel 1. Put the other phone plug into Digital Channel 2.
  • Place the track on a horizontal surface. Put the cart near the middle of the track and level the track by raising or lowering one end so the cart will not roll one way or the other. Remove the cart when the track is level.
  • Put the Motion Sensor at one end of the track. Place a flat surface (such as a book) exactly one meter away from the Motion Sensor. Adjust the target so that it can reflect the pulses from the Motion Sensor.

Equipment Setup

  • Clamp a block onto the table next to the end stop at one end of the track or place a large mass against the end of the track.
  • This will keep the track from sliding one way when the plunger spring pushes the cart the opposite direction (Why does the track tend to slide w/o this measure?).
  • Put the Motion Sensor at the other of the track.
  • Put a pencil mark on the edge of the track 15 cm in front of the Motion Sensor.
  • Measure the length of the plunger relative to the end cap of the dynamics cart. Record the plunger length x in the data section.
  • Fully compress the plunger spring on the cart, and lock the spring in position by pulling the end of the plunger bar upward slightly so one of its notches will ‘catch’ on the metal rail inside the cart’s end cap.

  • Put the cart on the track so the end of the plunger bar is against the end-stop.

PART III: Data Recording

1.Start recording data. (Click ‘Start’ in DataStudio)

2.Use the end of a pencil or similar object to tap down on the plunger release pin.

•Avoid getting your hand in the way of the pulses from the Motion Sensor.

•The cart will be pushed away from the end-stop by the plunger spring.

3.Stop recording data when the cart gets about 15 cm from the Motion Sensor.

•Catch the cart so it doesn’t run into the Motion Sensor.

  • Run #1 will appear in the Data list in the Experiment Setup window.
  • Determine the speed of the cart right after the spring expanded by analyzing the graph of speed vs. time.
  • Highlight the straight section of the graph and click the statistics button (the Σ symbol). You will see the min. and max. values of the section you highlighted. Record the greatest speed that the cart reached in your data section.
  • Repeat the data recording process two more times. You will take the average of the KE’s later.

Optional: Data Recording – Cart and Extra Mass

1.Put a mass bar in the accessory tray of the cart and measure the mass of the cart plus bar. Record the mass in the Lab Report.

2.Repeat the data recording process.

Analyzing the Data

  1. Calculate the kinetic energy of the cart using KE=½mv2.

3.Calculate the elastic potential energy based on k and xusing the equation EPE=½kx2. Record the value in the data section.

4.Determine the amount of energy lost and the %energy lost in the transfer from elastic to kinetic energy.

Data

Item / Value
Mass of cart (kg)
Spring constant “k” (N/m)
Plunger length “x” (m)
Run # / 1 / 2 / 3 / Average
speed (m/s)
KE (J)

Elastic Potential Energy = ______J

Difference from EPE to KE = ______J

% Loss of Energy = ______

Calculations(Show samples of each calculation…)

EPE=

KE=

Ave KE=

Difference from EPE to KE=

% energy lost = (EPE –KE)/EPE x 100

Questions

1.What happens to the speed of the cart as it moves down the track?

2.Which energy was larger, the elastic potential energy of the spring or the kinetic energy of the cart? Explain.

3.Where did the lost energy go? Does this lab disprove the Law of Conservation of Energy???

4.Why do you have to clamp a block down next to the track? Use Newton’s 3rd Law or Conservation of Momentum in your answer.

5.After you clamp the bock down, is momentum conserved in this experiment? Explain.

6.Use conservation of energy to determine how high in the air a 0.34kg ball will go if it is launched from a spring on the ground that is compressed 1.25m and has a spring constant of 4050 N/m. How would your answer change if the spring was compressed half as much?

Error Analysis

What was your % error? What sources of error exist in this lab, be specific?

Conclusion

What did you do? What did you find? What generalizations can you make?

GS21p. 1