# paper cones investigation

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

The aim of this work is to investigate the relationship between the time taken for a paper cone to fall and the mass of the cone.

Variables

Prediction

Since the theory suggests that

So the square of time should be directly proportional to the inverse of mass.

A straight line graph of t2 versus m-1 should give a straight line graph with a gradient of

All of these values will be measurable or known, except for the drag coefficient, c.

Method

Preliminary experiments

Determining a size of the paper cone:

Three unweighted paper cones were constructed from A4 paper and selotape:

w is the width (diameter) of the end circle of the cone.

h is the height of the cone.

w = 5cm, h = 5cm

w = 10cm, h = 5cm

w = 20cm, h = 5cm

They were dropped from a height of 1m and 2m and the time taken to fall measured with a stopwatch and recorded:

From an experiment viewpoint, the last cone, w = 20cm, h = 5cm, d = 2m would be best as it has the largest time to fall and hence the smallest percentage uncertainty in the measurement ...

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

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

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.

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.