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Name ______________________________________.
HWK Accuracy Precision Error Propagation
1.
The volume V of a cylinder of height h and radius r is given by the expression
V = r2h.
In a particular experiment, r is to be determined from measurements of V and h. The
uncertainties in V and in h are as shown below.
V
7 
h
3 
The approximate uncertainty in r is
2.
A.
10 .
B.
5 .
C.
4 .
D.
2 .
The density of a metal cube is given by the expression ρ 
M
where M is the mass and V is the
V
volume of the cube. The percentage uncertainties in M and V are as shown below.
M
12 
V
4.0 
The percentage uncertainty in the calculated value of the density is
A.
3.0 .
B.
8.0 .
C.
16 .
D.
48 .
(Total 1 mark)
1
3.
In an experiment to measure the acceleration of free fall at the surface of the Earth the following
results were obtained.
Acceleration of free fall / m s–2
7.69
7.70
7.69
7.68
7.70
The results are
A.
accurate and precise.
B.
inaccurate but precise.
C.
accurate but imprecise.
D.
inaccurate and imprecise.
(Total 1 mark)
4.
Which of the following is a valid statement?
A.
A measurement that is not precise can be accurate.
B.
A measurement that is precise is always accurate.
C.
A measurement that is not precise will always be inaccurate.
D.
Repeated measurements will always increase accuracy and precision.
(Total 1 mark)
2
5.
The magnitude of the mass of the universe is of the order of
A.
1020 kg.
B.
1030 kg.
C.
1040 kg.
D.
1050 kg.
(Total 1 mark)
6.
The masses and weights of different objects are independently measured. The graph is a plot of
weight versus mass that includes error bars.
These experimental results suggest that the
A.
measurements show a significant systematic error but small random error.
B.
measurements show a significant random error but small systematic error.
C.
measurements are precise but not accurate.
D.
weight of an object is proportional to its mass.
(Total 1 mark)
3
7.
Two lengths, a and b, are measured to be 51±1 cm and 49±1 cm respectively. In which of the
following quantities is the percentage uncertainty the largest?
A.
a+b
B.
a–b
C.
a×b
D.
a
b
(Total 1 mark)
8.
The current in a resistor is measured as 2.00 A ± 0.02 A. Which of the following correctly
identifies the absolute uncertainty and the percentage uncertainty in the current?
Absolute uncertainty
Percentage uncertainty
A.
± 0.02 A
±1 %
B.
± 0.01 A
± 0.5 %
C.
± 0.02 A
± 0.01 %
D.
± 0.01 A
± 0.005 %
(Total 1 mark)
Additional Questions:
THIS IS A PRACTICE ASSESSMENT. Show formulas, substitutions, answers (in spaces provided) and units!
For questions 1. through 4.
consider the line shown here:
1. What is the measured length of this line in mm? Use the amount of significant figures a wooden meter
stick is capable of supplying.
1. _________________
2. What is the precision of this measurement?
2. _________________
3. If the above line is one side of a perfect square, what is the area of that square, taking into account the
correct number of significant figures and the correct units? Note that area is length times width, and the
length equals the width in a square.
3. _________________
4. What is the raw uncertainty in your answer from problem 3?
4. _________________
4
A student measures a line to be 3.8 cm  0.1 cm.
5. Find the absolute uncertainty in the measurement.
5. _________________
6. Find the raw uncertainty in the measurement.
6. _________________
7. Find the fractional uncertainty in the measurement.
7. _________________
8. Find the percentage uncertainty in the measurement.
8. _________________
9. A flagpole is placed on the roof of a house. A student measures the flagpole to be 4.25 m  0.05 m. The
same student measures the height from the ground to the base of the flagpole to be 6.40 m  0.15 m. If
the flagpole is mounted vertically upward (straight up), how far is the tip of the flagpole above the
ground. Be sure to use significant figures and include a raw uncertainty with your answer.
9. _________________
10. A car travels 250 m  15 m in 12.2 s  0.2 s. Calculate its speed. Be sure to use significant figures and
include a raw uncertainty with your answer.
10. ________________
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