
Ex 2 Ex 3
Ex 4 


1. 
In an experiment, two variable
quantities, x and y were measured. 

The relation between x and y is
thought to be: 





The measured values were 

x /m
±0.01m 
y /s
±0.05s 
0.10 
0.64 
0.20 
0.90 
0.40 
1.27 
0.80 
1.80 
1.00 
1.90 



a) 
Plot a graph which could be used to verify the
relation between x and y. 
b) 
From the graph find the value of the constant, a. 
c) 
Add to the graph error bars for the first and last
results. 


2. 
In an experiment, two variable
quantities, x and y were measured. 

The relation between x and y is
thought to be: 





The measured values were 

x /cm
±0.02cm 
y /g
±0.25g 
0.67 
2.25 
0.80 
4.00 
0.90 
5.52 
0.95 
6.60 



a) 
Plot a graph which could be used to verify the
relation between x and y. 
b) 
Add error bars to the points on the graph. 
c) 
Use the graph to estimate the maximum and minimum
values of the constant, b. 

Give your final answer for b in the usual
form: 

b = value ±indeterminacy 
d) 
What physical quantity might b represent? 


3. 
A point source of light was placed at different
distances, r from a photoelectric cell. 

The current, I
generated by the cell was measured. 

It is thought that the relation between
I and r is of
the form 



where k and n are constants. 

Now, (as every ten year old child knows), taking
logs of both sides of this equation gives us 





The measured values were 

r /cm
±0.5cm 
I /mA
±2mA 
15 
108 
20 
61 
25 
39 
30 
27 
35 
24 
40 
15 
45 
12 



a) 
Plot a graph which could be used to verify the
relation between I and r. 
b) 
Use the graph to find the value of the
constant n 
c) 
Find the value of the constant k 
d) 
A significant error was made in one of the
measurements. 

Suggest a possible corrected value for this result. 
e) 
Add error bars to the points representing the
first and last results. 


4. 
Part 1 

Muons (also called µ mesons) are unstable particles. 

A muon decays into (changes into) an electron, a
neutrino and an antineutrino. 

The decay occurs at random but if we have enough
particles their rate of decay is predictable. 

An experiment was conducted to observe the rate of
decay of muons. 

The results are shown below. 



t /μs 
number of muons remaining
N 
0 
568 
1 
373 
2 
229 
3 
145 
4 
99 
5 
62 
6 
36 
7 
17 
8 
6 




Theory suggests that the equation which describes
this decay has the form 



where 

N_{o} is the number of
muons present at a given time 


N is the number of muons remaining
t seconds later 


λ is a
constant called the decay constant (for the
muons) 




Taking logs of both sides of the equation gives us 




a) 
Plot a graph of N against t. 
b) 
Use three points on the graph to show that the
equation of the graph has the form predicted by the
theory and, in doing this, calculate the value of the
decay constant. 
c) 
Use the equation to calculate the number of muons
remaining at t = 6·5µs 



Part 2 

A similar experiment was conducted using muons which
were moving at high speed relative to the
experimenter. 

The speed was very close to the speed of light. 

Einstein’s theory of relativity predicts that, in
this situation, time for the muons (which we will call
muon time t_{m}) will be different
from time as measured by the experimenter t_{e}
(see Time Dilation) 

Muons, of course, decay at a rate which depends on
their own time not the experimenter’s time. 

In this second experiment, it is found that at time
t = 6.5μs, as measured by the experimenter’s clock, the
number of muons remaining is 400. 



Einstein predicted that the relation between the
experimenter’s time and the muon’s time is given by 



where 

v (the speed of the muons relative to the
experimenter) = 2.9805×10^{8}ms^{1} 


c (the speed of light) = 2.9979×10^{8}ms^{1} 




Use your graph to show that these two experiments
give support to Einstein’s time dilation equation. 