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# paper cones investigation

Extracts from this document...

Introduction

Investigation Report

Aim

Theory

When an object is dropped in air, it accelerates. If it is allowed to drop far enough then it can reach its terminal velocity. This is the maximum velocity of the object during its fall and occurs when the upward force of air resistance acting on the object equals the weight of the object.

So at terminal velocity...

(P.31, Complete Physics, 1999, Pople, Oxford University Press, ISBN 0-19-914734-5)

(P.33, Physics 1, 2000, Cambridge University Press, ISBN 0-521-78718-1)

Looking for a formula for air resistance...

F = force of air resistance

ρ = density of air = 1.2kgm-3

c = coefficient of drag for the object / dimensionless

A = cross-sectional area of object hitting the air / m2

v = velocity of the object / ms-1

(http://damonrinard.com/aero/formulas.htm)

Looking for a formula for the weight of an object...

W = m.g

W = weight / N

m = mass / kg

g = acceleration due to gravity, 9.81Nkg-1

(P.55, Physics, 1991, Robert Hutchings, Nelson, ISBN 0-17-438510-2)

So putting these formulae together...

From the Physics AS course,

v = velocity

x = displacement

t =  time

so

References to the specification

Forces and Motion 2821

Forces, Fields and Energy 2824

Middle

Equipment list

A4 Paper

Scissors

Selotape

Bluetak (approx 50g)

Metre rule (giving a resolution of ±1mm appropriate for measuring, h.)

Stopwatch (giving a resolution of ±0.01s appropriate for measuring t.)

Electronic Balance

(giving a resolution of ±0.001g appropriate for measuring m.)

Results

Raw results tables including absolute uncertainties

Tables of calculated values e.g. means, percentage uncertainties

 m / kg t1 / s t2 / s t3 / s Mean t / s Range in t / s Uncertainty in t % uncertainty in t %Uncertainty in m 0.003 2.60 2.66 2.77 2.68 0.17 0.09 3 17 0.004 2.22 2.50 2.33 2.35 0.28 0.14 6 13 0.005 1.87 1.83 1.72 1.81 0.15 0.07 4 10 0.006 1.64 1.81 2.11 1.85 0.47 0.23 13 8 0.007 1.93 1.57 1.50 1.67 0.43 0.22 13 7 0.008 1.49 1.68 1.79 1.65 0.30 0.15 9 6 0.009 1.68 1.51 1.26 1.49 0.42 0.21 14 6 0.01 1.20 1.22 1.43 1.28 0.23 0.11 9 5 0.011 1.56 1.15 1.54 1.42 0.41 0.21 15 5 0.012 1.42 1.19 1.16 1.26 0.26 0.13 10 4 0.013 1.32 1.33 1.41 1.36 0.09 0.04 3 4 0.014 1.30 1.20 1.02 1.17 0.28 0.14 12 4 0.015 1.24 1.29 0.95 1.16 0.34 0.17 15 3 0.016 1.01 0.94 1.29 1.08 0.35 0.18 16 3

Analysis

Raw graphs of results

The trend shown here confirms a non-linear relationship between time and mass. It is consistent with a inverse relationship of some form.

There are no anomalous results to be dealt with.

Conclusion

Range of measurements and the number of readings taken

The range of measurements was limited to masses of a few grams. Clearly this limits the confirmation of the prediction to within this range. A larger range of masses would be required to confirm the relationship outside of the readings taken.

The number of readings taken (3 per independent value) was sufficient to enable an indication of the uncertainties in the measurement of time. A larger number of repeats (>30) would be required for a statistically significant sample to be taken to confirm the random nature of the uncertainties and their distribution.

Combined Uncertainty for the experiment

Using a simple sum of percentage uncertainties we get a worst case value of :

±32% (time) + ±17% (mass) + ±5% (drop distance) = ±54%

Note: the time uncertainty of ±16% is doubled because of the t2 nature of the relationship.

Validity of the results

The largest percentage difference between a data point and the best fit line for t2 versus m-1 was ±23%. This is more than accounted for by the combined worst case uncertainty for the experiment of ±54%.

Hence the results do indicate that the predicted relationship is plausible.

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

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## Here's what a star student thought of this essay

5 star(s)

### Response to the question

The writer has approached the investigation well. As a result, the writer has produced a well written report. All of the writers objectives have been clearly covered, therefore making their report clear and easy to follow. It was good that ...

### Response to the question

The writer has approached the investigation well. As a result, the writer has produced a well written report. All of the writers objectives have been clearly covered, therefore making their report clear and easy to follow. It was good that the writer was able to explore the theory behind the experimentation taking place. It was also good that the writer was able to explore ways to reduce error by carrying out a preliminary investigation, this being explained during the writers conclusion. Overall, this is a high quality report.

### Level of analysis

The language that the writer used is of a high standard. The area that the writer has investigated is not fully covered within the syllabus, but it's good that the writer was able to gain suitable information on the area within the research that they did. The writer used the correct terminology with regards to experimentation and the scientific background.

### Quality of writing

Spelling and grammar are of a high standard. The presentation of the report is clear and done to a really high standard.

Reviewed by cpdavis 13/03/2012

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