Apparatus
Large marble, adjustable support, runway, marker pen, metre rule, 50 cm rule, stop clock, safety goggles.
Method
- Set up the apparatus as shown in the diagram.
- With the marker pen mark a starting line, A, near the top of the runway.
- Likewise, mark a finishing line, B, near the bottom of the runway.
- Measure the distance between A and B with a meter rule. Record this distance in metres in a suitable table. This distance will remain unchanged throughout the experiment.
- Adjust the support so that the runway has a vertical height at A of 5 cm. Measure the distance with a 50 cm rule and record in the table.
- Place the marble at A. Release from rest and simultaneously start the stop clock.
- Stop the stop clock when the marble reaches B. Record the time taken in seconds in the table.
- Repeat twice more and then calculate the average time. Record in the table.
- Calculate the average speed using the equation: average speed = \(\frac{distance~travelled}{average~time~taken}\)
- Repeat the procedure for a total of 6 different vertical heights, increasing the height by 5 cm each time.
- Plot a graph of Average speed in m/s on the y-axis against Vertical height in m on the x-axis.
Safety
- place an obstacle, such as a stool, to keep feet from underneath the runway making sure the marble doesn鈥檛 fall on someone鈥檚 foot;
- make sure the marble doesn鈥檛 fall on to the floor and someone slips on it;
- secure the runway with a clamp in the centre of the bench, so it doesn鈥檛 fall off on to someone鈥檚 foot;
- wear safety goggles in case a marble hits someone in the eye.
| Vertical height of runway in cm | Distance travelled in m | Time taken in s (1) | Time taken in s (2) | Time taken in s (3) | Average time taken in s | Average speed in m/s |
| 5 | 1.75 | |||||
| 10 | 1.75 | |||||
| 15 | 1.75 | |||||
| 20 | 1.75 | |||||
| 25 | 1.75 | |||||
| 30 | 1.75 |
| Vertical height of runway in cm | 5 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
| Vertical height of runway in cm | 10 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
| Vertical height of runway in cm | 15 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
| Vertical height of runway in cm | 20 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
| Vertical height of runway in cm | 25 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
| Vertical height of runway in cm | 30 |
|---|---|
| Distance travelled in m | 1.75 |
| Time taken in s (1) | |
| Time taken in s (2) | |
| Time taken in s (3) | |
| Average time taken in s | |
| Average speed in m/s |
Graph
Error
The main cause of error in this experiment is reaction time when the person starts and stops the stop clock.
Error due to reaction time can be kept to a minimum by:
- repeating the timing for each height three times and calculating the average time for the marble to roll down the runway;
- ensuring that the time taken for the marble to roll down the runway is as long as possible. This can be done by:
- making the distance between A and B as long as possible;
- keeping the vertical height as small as possible, so that the marble doesn鈥檛 move too fast.
Conclusion
As the vertical height of the runway increases the average speed of the marble also increases, in line with our prediction.
However, we can say that the vertical height is not directly proportional to the average speed as the line of best fit is not a straight line through the origin.