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• Level: GCSE
• Subject: Maths
• Word count: 1161

# Measuring the Height of the PhysicsTower.

Extracts from this document...

Introduction

Measuring the Height of the Physics Tower

Introduction:

This assignment deals with the measurement of the height of the main tower of the Physics and Astronomy Building.  In order for this to be somewhat a challenge, the equipment available to first year students isn’t sophisticated at all.  However, this calls for creativity and some thinking.  There are many methods that one could use to measure the height and they all require basic tools and none in some cases.  There are four methods that are considered to be easy to perform.  First, one could drop an object from above and using the known acceleration and time measured could find the height. However, errors like unknown air resistance and wind could change the actual result.  Secondly, one could count the number of blocks making the building and multiply them by the individual length. This method relies on the assumption that all the blocks

Middle

Results:

 Run Distance Away (x) Angle (Ө) Person’s Height 1 23.05 m 69° 1.58 m 2 33.64 m 58° 1.58 m 3 46.85 m 52° 1.58 m 4 21.50 m 70° 1.70 m 5 28.10 m 63° 1.70 m 6 49.23 m 49° 1.70 m

Note that the value of (x) or the person’s height are measured up to two decimal digits according to the tape measure used.  Also the angle has been rounded off to the nearest since the protractor doesn’t provide a better precision than one single degree.

Calculations:

The total height of the tower is basically the height of the person in addition to the height of the remainder of the building. The height is considered to be from the main floor of McLennan Physical Laboratories Building and up to the top of the Burton tower excluding the secondary structure at the top.  According to the diagram above, we can use trigonometric ratios to find H1 and then add it to H2

Conclusion

Sample Run Error Calculation (Run # 4):

Errors for other runs were computed in the same manner, the following was obtained:

Run 1: ±0.89 m

Run 2: ±0.96 m

Run 3: ±1.18 m

Run 4: ±0.87 m

Run 5: ±0.90 m

Run 6: ±1.19 m

After some analysis, it is found that the average reading error is 1.00 m with 0.15 m standard deviation.

Random Error:

The random error could be done by saying that the error is half of the last digit that the instrument reads. So for x its ±0.005 m (0.5 cm) and for Ө its ±0.5°.  Using the same equation used above, we could find the random error in each run.

Run 1: ±0.45 m

Run 2: ±0.48 m

Run 3: ±0.59 m

Run 4: ±0.43 m

Run 5: ±0.45 m

Run 6: ±0.60 m

After some analysis, it is found that the average reading error is 0.50 m with 0.08 m standard deviation.

It is obvious to see that the reading error is exactly double of the random error. To obtain net error, one must add the two means of the two different errors for total error.

Conclusion:

The height of the Physics and Astronomy building is 59.08 ± 1.50 m.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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