Ticker-timers for investigating speed
Making ticker-timer charts can develop an understanding of speed-time graphs.
Apparatus and materials
For each student or student group
Ticker-timer with power supply unit
Health & Safety and Technical notes
In crowded laboratories, estimate the space needed by the tape puller and arrange the groups to avoid collisions. It may be impracticable for all groups to do this.
Self-adhesive and plain ticker-tape are both available. The self-adhesive version is more convenient for this experiment.
a One person should operate the ticker-timer switch while another walks away, pulling tape through the ticker-timer. The walker should speed up and then slow down and stop, while the tape is running through the timer.
b Look at the tape. The dots happen at regular time intervals, but sometimes they are close together and sometimes they are further apart.
c Cut across the tape through the dot that was made when the person started to move. Count ten dot-to-dot spaces. Cut it again. That gives you a short strip, which is a ten-tick-tape. (It might be hard to count spaces when the dots are very close together, and you will have to estimate the number of spaces.)
d Make a horizontal line along the bottom of a sheet of paper. Stick your ten-tick-tape near the start of the line. The first dot of the ten-tick-tape should be on the horizontal line. The line of dots should be vertical.
e Count ten more dot-to-dot spaces along the tape. Cut it again. Stick this 10-tick-tape alongside the first one.
f Cut the whole of the tape into ten-tick-tapes, to make a complete chart.
g Label the chart where the person pulling the tape was:
- going slowly
- moving fast
- speeding up
- slowing down.
h Your chart is a bit like a graph of speed against time.
- The time to make each tape was exactly the same. Your horizontal line represents time for the journey of the tape.
- The length of each ten-tick-tape depends on the speed. The higher the speed then the longer the tape. Add a vertical axis to your chart. This axis represents speed.
i Predict what the chart would look like if the tape travelled at a steady and slow speed. Also predict what it would look like if it travelled at steady high speed. Check your predictions. Make a tape for slow steady motion and use it to make a chart. Do the same for fast steady motion.
j Predict what the chart would look like if the tape travelled at speed that increased steadily. To test this prediction, start by pulling the tape very slowly but then let it get gradually faster.
k The motion of other objects such as toys, bicycle, car, falling weights could also be tried.
1 Provide students with squared (or graph) paper, so the ticker-timer strips are more easily aligned.
2 You will need to explain carefully the idea that the length of tape in each 'ten-tick' of time indicates speed.
3 If the speed of the tape increases steadily, the upper edge of the ticker-tape chart should form a straight line slanting upwards. Thinking about this should encourage students towards a difficult idea: a speed - time graph with a positive gradient indicates acceleration.
4 With more able students, you may want to develop the idea that the total area of the chart tape represents the total distance travelled.
The total distance travelled by the object is the full length of the tape and cutting it up does not alter this. If the tape was 1 cm-wide then the area of each strip would just be numerically equal to the distance travelled in the time represented by the strip. Adding together all the areas of the strips would give the area of the chart and so the area of the chart represents the distance travelled (for 1 cm wide strips).
The graph of velocity against time has time in seconds along the x-axis and speed in cm/s along the vertical axis. The area under the graph measures the distance travelled in centimetres. Areas under graphs measure the product of the values represented on the x and y-axis. On a velocity-time graph each vertical strip represents v Δ t and v Δ t = Δs , the distance travelled in time Δt.
Ticker-tape charts make a good introduction to integration as the area under a curve shows one application of calculus.
5 Finally, a different type of chart can be made. The tape of a moving object is placed on the bench and a second blank tape is laid alongside it. From this tape a piece is cut off equal to the distance travelled in the first 10-tick or 1/5 of a second and stuck down to start making a chart. Then a second piece of tape is cut from measuring the distance travelled on the first tape from the beginning of the motion to the end of 2/5 of a second and so on until all the motion tape is used. This tape chart shows a distance travelled against time.
If the speed is increased steadily, the top edge of this chart is not a straight line but rather it follows a curve (s = 1/2at2).
6 This experiment could be followed by "Simple motion experiments with a datalogger", which uses software to plot velocity - time graphs directly.
This experiment was safety-checked in April 2006