Predicting the motion of a falling card

Introduction

Educational data loggerThis experiment demonstrates how DrDAQ can be used to investigate how height effects the velocity of a free falling object. This experiment is very simple, and with PicoScope enables the data to be collected rapidly.

The experiment aims to identify and prove existing theories on speed and distance.

Equipment required

  • A PC with PicoScope installed
  • DrDAQ PC based data logger
  • A Bench timer light gate, we used one from Technology Supplies Ltd (product LA30-660):
    Technology Supplies Ltd.
    Phoenix House
    Tern Hill
    Market Drayton
    Shropshire
    UK
    Tel. 01630 637300.
  • A stand or clamp to hold the light gate.
  • Suitable leads and connectors.

Experiment setup

The idea is to drop a card of known length through the light gate and calculate the speed from the waveform collected in PicoScope.

card

The card needs to be black so that the signal recorded in PicoScope is sharp due to the light beam being interrupted cleanly. It is also necessary to fix two blobs of Blu-Tack to the card to give it some ballast in order for the card to fall straight.

set up

The output from the Lascells light gate is fed directly into the voltage input and ground of the DrDAQ, from within PicoScope it is immediately possible to see how blocking the light gate effects the voltage levels.

Carrying out the experiment

PicoScope is set up to trigger upon the change in voltage from the light gate, 1000 mV. A pre-trigger is added to show the effect the card has on the light gate in better detail.

results

Theory

The velocity of the card as it passes through the light gate can be calculated by dividing the distance over the time. The distance is a constant, i.e. the card length does not change, however the speed for it to pass through the light gate will depend on the height. The following equation is used:

equation

Where the length is a constant (10 cm) and the time will vary, depending on the time taken for the card to pass through the light gate.

Results

Height Time Velocity
10 cm 60.05 ms 1.6653 m/s
15 cm 49.99 ms 2.0003 m/s
20 cm 45.38 ms 2.2036 m/s
25 cm 41.44 ms 2.4134m/s
30cm 39.13 ms 2.555 6m/s
35 cm 37.18 ms 2.689 5m/s
40 cm 36.1 4ms 2.7671m/s

If this is plotted on a graph the relationship can be seen quite clearly:

graph

Discussion of results

This experiment clearly shows the relationship between acceleration and height fallen. It also demonstrates that the higher the card falls from the greater the final velocity when it passes through the light gate. From the graph it is possible to predict the maximum speed that the card is likely to fall at from the curve of the graph.