Chapter Uncertainty AS Level Cambridge Curriculum

Chapter Uncertainty AS Level Cambridge Curriculum

1. Uncertainty

2. Experimental Uncertainty
Random
Uncertainty
Systematical
Uncertainty
Through limitation of the scale on
an instrument/ through the way
the instrument is used
Instrument is faulty / being
used incorrectly (zero error)
Reduced by making multiple
measurement
Corrected by recalibrating the
instruments
Measurement will sometimes be
above or below the true value
Parallax error and
zero error

3. Precision
How tightly grouped the
data is
High precise : make several
measurement of a quantity
and they are all very similar
Less precise : if the
measurement are spread
widely around the average
Accuracy
How close overall data is to
the target value
High accuracy : if the value
is close to the true value
Less accuracy : if the value
is far to the true value

4. High precise
High accuracy
High precise
Low accuracy
Low precise
High accuracy
Low precise
Low accuracy

5. Four students performed an experiment to
measure the density of aluminium (2,7g/mL).
Which data is accurate but not precise?

6. (425 ± 0,3) N
Main Value Uncertainty
Maximum Value (425 + 0,3) N = 425,3 N
Minimum Value (425 - 0,3) N = 424,7 N
Percentage
Uncertainty
������????????????���
�????????????� �??????���
�100%
=
0,3
425
�100%=0,07%

7. Estimating Uncertainty
Uncertainty in Addition of Values
Uncertainty in Subtraction of
Value
Uncertainty in Multiplication or
Division of Value
Uncertainty in Values Raised to a
Power

8. Uncertainty in Addition of Values
An object with momentum (85 ± 2) Ns catches up with, and stick to
another object with momentum (77 ± 3) Ns. Find the total momentum
of the two objects and its uncertainty after collision.
Answer :
Momentum = (…. ± ….) Ns
Value = 85 + 77 = 162 Ns
Uncertainty = 2 + 3 = 5 Ns
% Uncertainty =
������????????????��??????
??????????????????� �??????���
�100%
% Uncertainty =
5
162
� 100%=3,1%
Therefore, the total momentum = (162 ± 5) Ns

9. Uncertainty in Subtraction of Values
A reading on a balance of the mass of an empty beaker is (105 ± 1)g.
After some liquid is poured into the beaker, the reading becomes
(112 ± 1)g. Deduce the mass of liquid added and its uncertainty.
Mass = (…. ± ….) g
Value = 112 – 105 = 7 g
Uncertainty = 1 + 1 = 2 g
% Uncertainty =
������????????????��??????
??????????????????� �??????���
�100%
% Uncertainty =
2
7
� 100%=29%
Therefore, the mass of liquid = (7 ± 2) g

10. Uncertainty in Multiplication of Values
A plane travels at a speed of (250 ± 10)m/s for a time of (18000 ± 100)s. Determine the
distance travelled and its uncertainty.
Answer:
�??????���=
�??????��??????���
�??????��
�??????��??????���=�??????��� � �??????��
Value = 250m/s x 18000s = 4,50 � 10
6
m
Uncertainty = Maximum value – value
Maximum value = 260m/s x 18100s = 4,71 � 10
6
m
Uncertainty =(4,71 � 10
6
m)−(4,50 � 10
6
m) = 0,2 � 10
6
m
% Uncertainties =
0,2
4,5
�100%=4,6%
Therefore, the distance = (�,��±�,�) ?????? ��
�
m

11. Uncertainty in Values raised to a Power
Determine the value of the kinetic energy, and its uncertainty, of a cyclist of mass
(63 ± 1)kg when travelling with speed (12,0 ± 0,5)m/s.
Answer:
�??????���??????� ����??????�=
1
2
� � � � � �
Value =
1
2
� 63 � 12 � 12=4500 ??????
Uncertainty = Maximum value – value
Maximum value =
1
2
� 64kg x 12,5m/s x 12,5m/s
Maximum Value = 5000 ??????
Uncertainty =(5000??????)−(4500??????) = 500??????
Therefore, the kinetic energy = ���� ±���??????
% mass =
1
63
�100%=1,6%
% speed =
0,5
12
�100%=4,2%
% Uncertainty = % mass + 2(% speed)
% Uncertainty = 1,6 + 2(4,2%) = 10%

12. Exercises

13. Challenge
A cuboid metal has a measured mass (4,70 ± 0,2)kg. Its dimensions are:
length (50,5 ± 0,2)cm, width (7,60 ± 0,08)cm, depth (5,02 ± 0,02)cm.
Deduce,
a.The volume of the cuboid, together with its uncertainty
b.The density of the metal of the cuboid