# Investigating free fall with a light gate

##### Demonstration

The acceleration of an object allowed to fall under the force of gravity is found by dropping a card vertically through a light gate. The emphasis of this datalogging experiment is on investigating the relationship between the velocity of the card and the distance it has fallen from rest.

#### Apparatus and materials

Light gate, interface and computer

Weighted card

Clamp and stand

Metre or half metre rule

#### Health & Safety and Technical notes

Clamp the light gate about 20 cm above the bench. Clamp a ruler so that the vertical distance may be measured from above the level of the light gate.

Cut black card to the precise length of 10.0 cm. Draw a pencil line across the width of the card at exactly half its length.

Measurements of the height fallen by the card should be made to this line rather than the lower or upper edge of the card. Adding two small blobs of Blutack, at the lower corners, will improve the stability of the card as it falls.

Configure the data-logging software to measure the transit time and calculate the velocity as the card passes through the light gate. A series of results is accumulated in a table. This should also include a column for the manual entry of distance measurements taken from the ruler.

#### Procedure Data collection
Hold the card above the light gate and next to the ruler so that its height above the gate may be measured carefully. Release the card so that it cuts through the light beam; a velocity measurement should appear in the table on the screen. Repeat this measurement from the same height several times; enter the height value in the height column of the table in the computer program.

Repeat this procedure for a new starting height 2 cm above the first.

Collect a series of measurements, each time increasing the height by 2 cm.

Analysis
Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the relative increase in values of velocity as greater heights are chosen.

The relationship between velocity and height fallen is more precisely investigated by plotting a XY graph of these two quantities. (Y axis: velocity; X axis: height fallen.) Use a curve matching tool to identify the algebraic form of the relationship. This is usually of the form 'velocity is proportional to the square root of height'.

Use the program to calculate a new column of data representing the square of the velocity. Plot this against height on a new graph. A straight line is the usual result, showing that the velocity squared is proportional to the height fallen.

#### Teaching notes

1 One of the chief values of real-time data-logging, exemplified here, is the interaction between the collection and simultaneous display of results. These can be used to prompt students' thinking. You can orchestrate discussion as the experiment proceeds. If you do this as a class experiment, students should be prompted to ask questions about the results and the process involved in collecting them.

2 Small variations between individual results should be observed and possible sources of error discussed. For example, how 'clean' was the release of the card, how precise was the height measurement, was the fall wobble-free? and so on. The visual display of results on a bar chart helps to show the significance of these variations, compared with overall trends in the relationship between velocity and height. The chart also makes it very easy to spot anomalous results due to the card wobbling or snagging on the ruler as it falls. The software usually facilitates the deletion or hiding of such values.

3 Software provides several alternative approaches to analysis. Two examples are described here; a straightforward plot of the collected data, velocity against height, and a second plot involving calculated data.

The first graph yields a curve which may be conveniently evaluated using a software curve-fitting tool. (It is best to give students tools which allow them to experiment with simple general forms such as quadratics and power laws rather than polynomial fits whose physical significance is hard to interpret.)

The second graph yields a straight line which lends itself easily to conventional analysis using concepts such as gradient and intercept.

Note: The discussion here has assumed that the software is capable of calculating and showing 'velocity' as the primary measurement. Physically the system actually measures transit times for the card passing through the light gate. It is necessary for the user to enter into the program the length of the card (the distance travelled during the transit time) at the beginning of the session. Calculations may then be performed as a matter of routine during the experiment. Eliminating this calculation step from the experimental procedure allows thinking and discussion to focus on the relationship between velocity and height fallen.

This experiment was safety-checked in May 2006