Graphs and Relationships Year 11 Physics
The first graph shows the relationship where
y is proportional to x
25
20
y
in symbols y α x
or y = gradient times x
The graph of this relationship
is a straight line
30
15
10
5
0
0
5
10
15
20
x
The second graph shows the
relationship where
Y is inversely proportional to x
0.7
In symbols y α 1/x
0.4
0.6
y
0.5
0.3
This means that when the x variable
is multiplied by a certain factor then
the y variable will be divided by the
same factor. So as x increases, y will
decrease by the same factor.
0.2
0.1
0
0
10
20
x
This graph is a hyperbola
30
The third graph shows the
relationship where
6000
y is proportional to the square of x
4000
y
5000
In symbols y α x2 This means that
when the x variable is multiplied by
a certain factor then the y variable will
be multiplied by the square of the factor.
3000
2000
1000
0
0
1
This graph is a parabola
2
3
4
0.6
0.8
x
The fourth graph shows the relationship
where
The graph is similar to a hyperbola
but much steeper.
300
250
200
y
Y is inversely proportional to the
square of x
In symbols y α 1/x2 ie when x is
doubled then y changes by a factor
of one quarter.
150
100
50
0
0
0.2
0.4
x
Square Power Law
Ball rolling down a slope
When a ball rolls down a slope from rest, it travels a distance d in time t.
The results table below shows values of the distance traveled for different values of the
time.
a) Use graph paper to plot a graph of the distance d down the slope versus the time taken
t. Though d is the independent variable plot it along the vertical axis to aid the analysis.
t (s)
d (m)
t2 (s2)
1.41
0.10
2.00
0.20
2.45
0.30
2.83
0.40
3.16
0.50
3.46
0.60
3.74
0.70
4.02
0.80
4.24
0.90
4.47
1.00
b) Describe the shape of the d versus t graph.
c) Calculate the values of t2 in the last row of the results table.
d) On the same graph paper plot d against t2.
e) Describe the shape of the last graph and the relationship it shows.
f) Calculate the slope of the last graph and include its unit.
g) Write down the empirical formula connecting d and t2.
Inverse Proportion Law
A loaded trolley of mass M is accelerated along a smooth surface by a hanging mass with
acceleration a. The acceleration for different masses are recorded below. (M includes
mass of trolley, added masses and accelerating mass)
M (kg)
a (m/s2)
1/M
0.50
5.0
0.75
3.3
1.0
2.5
1.25
2.0
1.5
1.7
1.75
1.4
a) Use graph paper to plot a (vertical) against M.(horizontal)
b) Describe the shape of the graph.
c) Calculate the reciprocal of the systems mass in the last row of the table.
d) Use the same paper to plot a versus 1/M
e) Describe the shape of the graph and the relationship between a and 1/M
f) Calculate the slope of the graph and state its unit
g) Write down the empirical formula connecting a and M
2.0
1.3
Proportionality
A 100kg rock falls from a cliff. The speed it travels at the end of each second is recorded
below.
Speed 0
(m/s)
Time 0
(s)
10
20
30
40
50
60
70
80
90
100
1
2
3
4
5
6
7
8
9
10
a) use graph paper to plot a graph of speed (v) versus time (t)
b) describe the shape of the graph
c) calculate the slope of the graph and include it’s unit
d) write down the empirical formula connecting v and t
e) what (sensible) name would you give the slope? What is its value?
Inverse square law
The brightness of a beam of light gets weaker as distance increases by the inverse square
law. The table below shows the values of light intensity (I) and distance (d)
Distance
(d) metres
Light
intensity
(I)Lumens
0.2
0.3
0.4
0.5
0.6
0.7
240
110
62
40
26
20
1/d2
a) Complete the third row of the table.
b) Plot a graph that will prove the inverse square law hypothesis.
c) Calculate the gradient of the straight line graph.
d) Hence write down the mathematical relationship between I and d.
e) Use your graph or the equation to calculate the intensity of light 0.35m from the bulb.