# Investigating energy transfers in a pendulum

Demonstration

When a pendulum is displaced, it gains gravitational potential energy due to its increased height. When subsequently released, this energy becomes transferred to kinetic energy. This datalogging experiment explores the relationship between these changes of energy.

#### Apparatus and materials

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

#### Health & Safety and Technical notes

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 kinetic energy. 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 kinetic energy 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
a 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.

b Enter 1.0 cm in the 'height fallen' column.

c Repeat this procedure for heights of 2, 3, 4 and 5 cm.

Analysis
Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the increase in values of kinetic energy as the height fallen is increased.

Investigate the relationship between kinetic energy and height fallen more precisely by plotting an XY graph of these two quantities. (Y axis: kinetic energy; X axis: height fallen.) This usually gives a straight line indicating proportionality. Use a curve-matching tool to identify the algebraic form of the relationship.

The gravitational potential energy lost depends in direct proportion upon height fallen. Therefore, the straight line graph indicates that kinetic energy gained is proportional to potential energy lost.

#### Teaching notes

1 Students can add a further column to the table, to calculate the potential energy lost from the height fallen, 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 potential energy should yield values numerically the same as the corresponding kinetic energy. This would support the law of conservation of energy.

2 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-checked in May 2006

#### User suggestion

This experiment is much more successful if the pendulum is made with a cylinder rather than a sphere. This will mean you don't have to make sure that the light gate passes through the centre of the sphere (to calculate the speed of the pendulum, you need to know its diameter), as the cylinder has a uniform diameter.

Page last updated on 05 October 2011