Section 2.1
Measuring in S.I.
Making and Recording Measurements
Accuracy

The closeness of a measurement to the accepted value for a
specific physical quantity.

Accuracy is expressed as an absolute error or relative error
Making and Recording Measurements
Absolute Error:
The difference between the measured value and the accepted
value.
Formula
Ea=
O-A
Ea : Absolute Error
O : observed or measured value
A : accepted value
Making and Recording Measurements
Absolute Error Example:
If your actual weight was 25 kg and your scale reads 23 kg,
what is your absolute error?
Ea=
O-A
Ea=
23 kg – 25 kg
Ea =
– 2 kg
Ea=
2 kg
Making and Recording Measurements
Relative Error:
The difference between the measured value and the accepted
value as a percentage
E r=
O-A
x 100%
E r=
A
Er : Relative Error
O : observed or measured value
A : accepted value
Ea
A
x 100%
Making and Recording Measurements
Relative Error Example:
If your actual weight was 25 kg and your scale reads 23 kg,
what is your absolute error? What is your relative error?
Er =
O-A
x 100%
Er =
25 kg
A
Er =
23 kg – 25 kg
25 kg
2 kg
x 100%
Er =
x 100%
8.0 %
Making and Recording Measurements
Precision
The agreement of several measurements that have been made
in the same manner.
Tolerance:
The degree of precision obtainable
Making and Recording Measurements
Accurate or Precise?
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Example of the differences between precision and accuracy for a set of
measurements:
Four student lab groups performed data collection activities in order to
determine the weight of some unknown rock
Group
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
AVG
1
34
612
78
126
413
132.6
2
126
127
126
128
125
126.4
3
20
500
62
980
938
500
4
502
501
503
498
499
500.6
Suppose the accepted value for the weight is 500 g.
Then we would classify each groups’ trials as:
Group 1: Neither precise nor accurate
Group 2: Precise, but not accurate
Group 3: Accurate, but not precise
Group 4: Both precise and accurate
Uncertainty in Measurement
4 types of lab errors:
Human Error: You screwed up!!
Method Error: You used a different method to measure each
time so you get different results
Uncertainty in Measurement
4 types of lab errors:
Parallax Error: Line of sight error
Example: Hold a pencil at arms length and look at it with one
eye closed. Now close the open eye and open the other. Notice
how the pencil appears to shift? This can cause mistakes in
measurements when reading metersticks and other equipment.
Try to avoid parallax errors.
Try to avoid parallax errors.
Incorrect: viewing the
meniscus
from an angle
Correct: Viewing the
meniscus
at eye level
Uncertainty in Measurement
4 types of lab errors:
Instrument Error:
Instrument error is caused by using measurement instruments
that are flawed in some way.
Why Is there Uncertainty?
 Measurements are performed with instruments.
 No instrument can read to an infinite number of decimal
places.
Which of these balances has the greatest uncertainty in
measurement?
Solving Physics Problems
Relationship between quantities
Direct Proportion:


As one quantity increases, the other increases.
Graph is a Straight Diagonal line
Relationship between quantities
Inverse Proportion:


As one quantity increases, the other decreases
Graph is a CURVED line
Steps to solving physics problems:
1.
2.
3.
4.
5.
6.
Read the problem and draw or sketch it
Write down “What you know” from the problem
Determine the “working equation” (SHOW WORK)
Substitute in the given data (SHOW WORK/UNITS)
Solve the equation: Mathematically (SHOW WORK)
a.
Box-In Final Answer!!!! (Don’t make me search for
your answer or you will not like your grade)
Check for accuracy and reasonableness (Think!!)
Kinds of Quantities
Scalar
Quantity has only magnitude
a.
A number with units
b.
Example: Speed, Distance, Mass
Vector
Quantity has magnitude and direction
a.
A number with units and a direction
b.
Example: Velocity, Displacement, Force
2.1 Homework (Page 37-38 in textbook)
• See Packet for questions
• Put problems on separate sheet of paper.