- Level: AS and A Level
- Subject: Science
- Word count: 1199
Making sense of data
Extracts from this document...
Introduction
Making sense of data
Trolley project
Data Provided:
Height (m) | Time (s) | |
1 | 2 | |
0.088 | 1.89 | 1.92 |
0.106 | 1.48 | 1.5 |
0.128 | 1.28 | |
0.145 | 1.14 | 1.14 |
0.163 | 1.02 | 1.03 |
0.182 | 0.953 | 0.957 |
0.198 | 0.883 | 0.887 |
0.215 | 0.833 | 0.836 |
0.236 | 0.793 | 0.795 |
0.252 | 0.753 | 0.754 |
0.271 | 0.721 | 0.72 |
0.291 | 0.695 | 0.696 |
0.311 | 0.666 | 0.66 |
The experiment I have chosen to analyze is a test to see how changing the height of a slope will affect the time it takes for a trolley to pass through a set of light gates. I hope to explore the data and consider what other conclusions can be drawn from it. To do this I must first ask the relevant questions, such as:
- What is the average time for each height?
- What is the average velocity through the light gates for each height?
- What is the final velocity for each height?
- What is the angle of the slope for each height?
- What is the speed at the first and second light gate?
- What is the acceleration?
- Is the ramp a smooth plane or will friction slow down the trolley, if so what is the coefficient of friction?
- How far up the slope are the light gates?
Middle
Using logs I know that: (Where (t)=time, (h)= height and (n) and (a) are unknowns)
I know that the formula of a straight line is, so if I substitute the logs we get,
Where (t)= y axis (n) = gradient, (h) = x axis and (a) + the y intercept.
Before I plot my graph I need to find the logs of the mean heights and times, these are shown in the table below.
log avg time | log Height (m) |
0.644482 | -2.430418465 |
0.3987761 | -2.244316185 |
0.2468601 | -2.055725015 |
0.1310283 | -1.931021537 |
0.0246926 | -1.814005078 |
-0.0460439 | -1.703748592 |
-0.1221676 | -1.619488248 |
-0.1809225 | -1.537117251 |
-0.2306718 | -1.443923474 |
-0.2830263 | -1.378326191 |
-0.3278099 | -1.305636458 |
-0.3631243 | -1.234432012 |
-0.4109803 | -1.167962367 |
From these values I can then draw the graph.
From the formula , I can get an average gradient of -1.2304 and a y intercept of -1.7311.
Conclusion
As well as height another factor influencing the velocity between the light gates is the angle of the slope. I can calculate this using trigonometry.
For all of the other heights,
Height (m) | Angle |
0.088 | 2.521828 |
0.106 | 3.0381 |
0.128 | 3.669438 |
0.145 | 4.157592 |
0.163 | 4.674791 |
0.182 | 5.221139 |
0.198 | 5.681589 |
0.215 | 6.171221 |
0.236 | 6.776691 |
0.252 | 7.238508 |
0.271 | 7.787533 |
0.291 | 8.366234 |
0.311 | 8.945796 |
Using Excel formula (=ASIN(K3/2)*180/PI())
I can then plot the graph
From the graph I can see that the velocity and the angle are directly proportional. This means that as the angle is greater then the velocity is too.
If I resolve the forces involved I can find the acceleration between the light gates as well.
Using height 0.088m
I know the speed is 0.52m/s
I know g(gravity) = 9.8
I know theta = 2.52
This means that acceleration is 0.43. This is only the theoretical acceleration as it will change but I will take this as a constant throughout the slope.
This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.
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