To Find Out How The Launch Height Of a Roller Coaster Affects Its Average Speed.

Speed² = 0.00352 * 0.2 * 9.81

0.5 * 0.00352

Speed² = 3.924 m/sec

Speed = V3.924 m/sec

Speed = 1.981 m/sec.

Launch height = 0.25m

Speed² = 0.00352 * 0.25 * 9.81

0.5 * 0.00352

Speed² = 4.905 m/sec

Speed = V4.905 m/sec

Speed = 2.2147 m/sec.

Launch height = 0.3m

Speed² = 0.00352 * 0.3 * 9.81

0.5 * 0.00352

Speed² = 5.886 m/sec

Speed = V5.886 m/sec

Speed = 2.426 m/sec.

Results

Height (cm)

Time 1(secs)

Time 2 (secs)

Time 3 (secs)

Average Time (secs)

30

.15

.25

.16

.18

25

.38

.10

.50

.44

20

.62

.43

.53

.575

5

2.06

2.10

.66

2.08

0

2.85

3.25

2.62

2.735

Analysis.

The results show that as the start height increases, the average time gets quicker. This is shown on the bar graph of these results, graph 1, as the X value (Start height) increases, so does the Y value (Average Time), the bars get taller. I have shown in the table above that two results were anomalous; this may have been due to the timing being imprecise which is likely, as the distance is not very long and it is hard to start the timer as soon as the ball starts travelling the 2meters and stop it again as soon as it finishes. Also, it may have been because the pipe that the ball travels down before I start timing it was not pointed directly at the finish point, if it was travelling diagonally, it would have taken a longer time to get there. This is why I did three repetitions of each height. However, Graph 2 shows me that the average time recorded for a height of 20cm is shorter than it should be. This may be due to any of the reasons I have said before.

I will work out the speed the ball was travelling at from these results. The ball was timed over a distance of 2 meters. I will compare these results with the expected speeds that I worked out in my prediction.

Height (m)

Distance (m)

Time (s)

Speed (m/sec)

Predicted Speed (m/sec)

0.30

2

.18

.695

2.426

0.25

2

.44

.389

2.2147

0.20

2

.575

.270

.981

0.15

2

2.08

0.962

.7155

0.10

2

2.735

0.731

.4

The higher the start height is, the faster the ball will travel across the 2-meter distance. The line graph, Graph 3 slopes upwards towards the greatest start height, this means that as the start height increases, and so does the speed. This is because, the Gravitational Potential Energy is equal to the mass of the vehicle x height x 9.81 so an increase in any of these three values will increase the GPE. The GPE becomes Kinetic energy (which determines how fast the ball will travel) when the ball starts to move. This explains why the speed increases as the start height increases.

These results also show that the actual speed of the ball was much slower than the predicted speed. This is also shown on graph 4. This will be because the calculations that I used to work out the expected results did not account for friction that definitely occurred in the actual experiment. Also, the times may have been recorded wrongly during the actual experiment, as the distance (2m) was quite short and it is difficult to record accurately as it passes so quickly.

The results support my simple prediction, which states that 'the higher the launch height is, the faster its average speed will be'. (It being the ball). However, the results do not support my quantitative prediction that I would get these speeds:

Height (m)

Speed (m/sec)

0.1

.4

0.15

.7155

0.2

.981

0.25

2.2147

0.3

2.426

My results showed that in the experiment, the ball travelled much slower, although graph 5 shows that the pattern that the actual results follow is the same as the expected results. This proves that my experiment went well and that the results were accurately measured and recorded. The actual results were slower than expected because friction was not accounted for in the calculations to find the predicted results.