measurements physics

1. Measurements
slides courtesy of Dr. Gamag

2. Learning Goals
• Be familiar with the SI units.
• Be familiar with the frequently used prefixes for SI units.
• Change units.

3. Learning Goals
 Differentiate accuracy from precision
 Differentiate random errors from systematic errors

4. Units
 How many people are in this classroom?
 What’s the temperature at the moment?
 What’s your height?
 How long does it take to walk from here to the
bookstore?
 How heavy is the Physics textbook?
Measurements

5. Standard Unit (SI / MKS)
meter kilogram second
Measurement Approximate value
Size of cells in most living organisms 1 x 10-5 m
Distance of Earth to nearest star 4 x 1016 m
Electron mass 9 x 10-31 kg
Sun’s mass 2 x 1030 kg
Time between normal heartbeats 8 x 10-1 s
Measurements

6. Prefixes

7. Prefixes

8. Unit Conversion
 Choose a conversion factor that will make the units
cancel, leaving the answer in the correct units.
Convert 1.34 kg to grams:
1.34 kg
103 g
1 kg
= 1340 g
Convert 43 km/h to m/s:
43 km
1 h
103 m
1 km
1 h
60 min
1 min
60 s
= 12
m
s

9. Uncertainty in Measurements
 Scientists share their results that are reported with an
uncertainty.
 A new measurement that is within the margin of uncertainty
confirms the old measurement.
Acceleration due to gravity is g = 9.80 ± 0.02
m
s2
Acceptable measurements range from 9.78 − 9.82
m
s2

10. Uncertainty in Measurements

11. Significant Figures
Multiplication or Division : fewest significant figures
Addition or Subtraction : fewest digits to the right of
the decimal point

12. Drill: Significant Figures
Here .

13. Accuracy vs. Precision
How precise and accurate are the
measurements of the three
students?
Spring elongation measured by three students. Data averaged
over five trials.

14.  It is the degree of exactness of a measurement.
 Student 3’s measurements are the most precise, within ±0.1
cm. The measurements of the other two students are less
precise because they have larger uncertainties.
 Precision depends on the instrument and
technique used to make the measurement.
 Device with the finest division on its scale
produces the most precise measurement.
Precision: how close are the data to each other?

15.  Precision: degree of exactness of a measurement
 Least count: smallest value that can be measured by the
instrument. Measured values are good only up to this value.
Precision: Least Count

16. Accuracy
 how well the results of a measurement agree with the “real”
value
If the real length of the spring had been
14.8 cm, then student 2 would have been
most accurate and student 3 least accurate.
Student 3 may be precise in
measuring but
he is the least accurate.

17. Precision versus Accuracy
Precision: closeness of the measurements to each other
Accuracy: closeness of the measurements to the true value

18. Systematic Errors vs. Random Errors
 Systematic Errors - consistent inaccuracies in the
result of an experiment that may be incurred due to
the equipment or faulty experiment procedure
e.g. misalignment, wrong calibration, negligence of
friction
 Random Errors - errors in measurement due to the
precision of the instrument or the experimenter’s
inability to do the measurements uniformly
e.g. stop watch’s precision, response time of
experimenter

19. Chapter 1 Exercise
a) Convert the following measurements to SI units
i. 42.3 cm
ii. 214 μg
iii. 57 ns
b) Rank the following mass measurements from least to
greatest: 11.6 mg, 1021 μg, 0.000006 kg, 0.31 mg.
c) The length of a room is 16.40 m, its width is 4.5 m, and
its height is 3.26 m. What is the volume enclosed by
the room?