Investigating energy transfers in a pendulum

Demonstration

When a pendulum is displaced, it stores energy gravitationally due to its increased height. When subsequently released, this energy is stored kinetically. This datalogging experiment explores the relationship between these changes to the ways that energy is stored.

Apparatus and Materials

• Light gate, interface and computer
• Pendulum
• Stand, clamp and boss
• Ruler in clamp
• Micrometer
• Electronic balance

Health & Safety and Technical Notes

Read our standard health & safety guidance

Set up the apparatus so that the stationary pendulum bob hangs exactly in front of the light sensor, interrupting the light beam.

Connect the light gate via an interface to a computer running data-logging software. The program should be configured to obtain measurements of speed, from which energy stored kinetically can be calculated (by hand or by the program). These are derived from the interruption of the light beam by the pendulum bob: this moves a distance equal to its diameter during the interruption time.

The internal calculation within the program requires the mass and diameter of the bob to be entered into the software, so that the velocity of the bob and energy stored kinetically are calculated. Measure the diameter using a micrometer. Measure the mass using an electronic balance with a sensitivity of 0.01 g. Accumulate the series of results in a table. This should also include a column for the manual entry of displacement height measurements, taken from the ruler.

Procedure

Data collection
1. Displace the bob so that it is raised 1.0 cm above its rest height as shown above. Hold the bob against the ruler. Note the reading for the point of contact which is on a level with the centre of the bob. Release carefully and allow it to perform ONE swing to and fro. This should produce two lines of data in the table, corresponding to the forward and back parts of the swing. Repeat this five times. The table shows ten values.
2. Enter 1.0 cm in the 'change in height' column.
3. Repeat this procedure for heights of 2, 3, 4 and 5 cm.
Analysis
4. Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the increase in values of energy stored kinetically as the change in height is increased.
5. Investigate the relationship between energy stored kinetically and change in height more precisely by plotting an XY graph of these two quantities. (Y axis: energy stored kinetically; X axis: change in height.) This usually gives a straight line indicating proportionality. Use a curve-matching tool to identify the algebraic form of the relationship.
6. The change in the energy stored gravitationally depends in direct proportion upon the change in height. Therefore, the straight line graph indicates that energy stored kinetically gained is proportional to change in energy stored gravitationally.

Teaching Notes

• Students can add a further column to the table, to calculate the change in energy stored gravitationally from the change in height, using m g Δh. Care is needed with units. In view of the small values of energy, it may be useful to calculate energy values in millijoules. Calculation of changes to the energy stored gravitationally should yield values numerically the same as the corresponding energy stored kinetically. This would support the law of conservation of energy.
• If the results are less than convincing, discuss the potential sources of error. Prime suspects must be the measurements performed using the ruler, micrometer and scales.

This experiment was submitted by Laurence Rogers, Senior Lecturer in Education at Leicester University.

This experiment was safety-tested in May 2006