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Making sense of data

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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

image00.png

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?
...read more.

Middle

image18.png

Using logs I know that: (Where (t)=time, (h)= height and (n) and (a) are unknowns)

image19.png

image20.png

image03.png

I know that the formula of a straight line isimage21.png, so if I substitute the logs we get,

image03.png

image21.png

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.

image02.png

From the formula image03.png, I can get an average gradient of -1.2304 and a y intercept of -1.7311.

...read more.

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.

image08.png

image09.png

image10.png

image11.png

image13.png

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


image14.png

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

image15.png

image16.png

image17.png

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.        


...read more.

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