VCE Physics Unit 1

1
VCE PhysicsUnit 1

• Analysis of an Experiment
• An introduction to Experimental Methods in Physics

2
Introduction
Experiments, in any field of science, are aimed
at collecting results, analyzing them and finding
relationships between the measured and/or
collected results.
The ultimate experiment is one that collects data
from just a few trials which, after analysis,
allows the development of a universal law
(usually expressed as a mathematical equation)
which is applicable anywhere, anytime.
The classic example of this is Newtons Law of
Universal Gravitation which, it is said, he
worked out by watching apples fall to the ground.
The aim of THIS exercise is to investigate water
flows from cans and develop mathematical rules or
laws which can predict how water will flow out of
any can, anywhere, anytime..
Before proceeding we need to take a small
mathematical diversion.
3
A Mathematical Diversion
The best way to find out whether two quantities
are mathematically related is to GRAPH them. Lets
call the two quantities y and x. We
collected the following data.
Plotting this data gives the following graph.
This is a straight line graph, indicating y ? x.
(y is directly proportional to x) The general
equation for a straight line graph is y mx c,
(where m slope or gradient and c y
intercept). The slope (20 6)/(9 2) 14/7
2 And the y intercept 2 So y 2x 2. We
now have a LAW that will allow us to work out any
value for y from a chosen value of x.
4
Cans, Water and Holes
The experiment investigated the time it took for
various depths of water to empty from holes (of
various diameters) punched into the bottom of
cans. You would expect that the time it took to
empty the can would depend upon 1. The diameter
of the hole, and 2. The depth of the water
To investigate the relation between time to empty
and hole diameter, 4 large cylindrical cans were
filled with the same volume of water and allowed
to empty through holes of varying diameter. The
time taken for each to empty was recorded.
To investigate the relation between depth of
water and time to empty, the same cans were
filled to different depths. The time taken for
each to empty was recorded.
5
Experimental Results
The results of the experiments were recorded and
presented in Table 1 below
The times quoted were taken by a hand operated
stopwatch. This timing method introduces an error
of ? 0.1 sec for each reading.
6
A First Analysis
The data collected and shown in Table 1 contains
the relationships between hole diameter and time
to empty and between water depth and time to
empty, but they are not obvious simply by looking
at the numbers. We need to ANALYSE the data.
ANALYSIS No. 1 HOLE DIAMETER VERSUS TIME TO EMPTY
The data (in Table No 1) has 3 variables (water
depth, hole diameter and time to empty). In
order to study the relation between hole diameter
and time to empty we need to hold the third
variable (water depth) fixed. So Table No 2
contains information on hole diameter and time to
empty for a fixed depth of 30.0 cm.
7
A First Graph
Just by looking at Table No 2, it seems that
there is an INVERSE RELATIONSHIP between hole
diameter and time. This means as hole diameter
goes up, time to empty goes down. But what is the
EXACT relation between diameter and time ? The
only way to find out is to plot a graph.
GRAPH No 1
Hole diameter is the independent variable and is
plotted on the horizontal axis. Time to Empty is
the dependent variable and is plotted on the
vertical axis.
8
An Inverse Relationship

• Graph No 1s shape definitely indicates an
  inverse relationship exists between time and
  diameter.
• But there are two types of inverse relations that
  could exist.
• t ? 1/d, or
• t ? 1/d2
• So which one is it ? More investigation is
  needed.
• This requires further manipulation of the data
  and further graphs.

Table No 3.
0.67 0.50 0.33 0.20
1.5 2.0 3.0 5.0
73.0 41.2 18.4 6.8
0.44 0.25 0.11 0.04
If one of the graphs (t against 1/d or t against
1/d2 ) produces a straight line , we will have
established an exact mathematical relationship.
ie. A LAW relating t and d.
9
A Second Graph
Plotting a graph of Time to Empty against 1/d
Should the point (0,0) be on the graph ? Yes,
because because as d approaches infinity (?) the
value of 1/d approaches 0. An infinitely large
hole will take no time to empty.
GRAPH No 2.
This graph is NOT a straight line. Thus we must
conclude that t is NOT ? to 1/d.
10
A Third Graph
Plotting a graph of time to Empty against I/d2
GRAPH No 3.
Within experimental limits, This graph IS a
straight line. Thus we can say t ? 1/d2.
We need to convert the proportionality (?) to an
equation in order to formulate the LAW which
relates t and d.
11
A Law Relating t and d
Having determined that t ? 1/d2. We need to
convert this to an equation. This is done by
recognizing the graph is a straight line with
general formula y mx c, where y t, x
1/d2, m slope and c y intercept.
Slope Rise/Run
(73.0 6.8)/(0.44 0.04). 66.2/0.4
165.5 And y intercept 0
Thus equation becomes t 165.5/d2.
Thus we have developed a LAW which allows us to
predict the time to empty a 30.0 cm depth of
water for ANY diameter hole.
12
A Second Analysis
ANALYSIS No 2 WATER DEPTH VERSUS TIME TO EMPTY
With a fixed hole diameter we can investigate the
relationship between Water Depth (h) and Time to
Empty (t) Table No 4 contains information for
various depths of water and time to empty for a
fixed hole diameter of 1.5 cm.
Graphing this information, we get
GRAPH No 4
13
A Parabolic Relationship
Graph No 5 is shaped like a parabola laid on its
side.
Sideways Parabola
Normal Parabola
General Formula of this line is y2 x. Or y
?x
General Formula of this line is y x2.
So graph No 5 appears to show a relationship of
the form Time to Empty (t ) ? square root of
Depth (?h) Further investigation is needed.
14
A Second Graph
To determine whether the relation we suspect is
true, we need to plot a graph of t against ?h. To
plot the graph we need data
The graph IS a straight line, thus our guess
about the relationship is true.
15
A Law Relating t and d
Having determined that t ? ?h, we need to convert
this to an equation. The general equation for a
straight line is y mx c, with y t , x ?h,
m slope and c y intercept.
Slope Rise/Run (73.0 13.5)/(5.48
1.00) 59.5/5.48 10.86
And y intercept 0
Thus the equation becomes t 10.86?h
We have now developed a LAW to predict the Time
to Empty ANY depth of water from a hole 1.5 cm in
diameter.
16
THE END