Measurements, Errors, Data Analysis

Question 1

Measurement

Answer 1

A scientific comparison of a physical quantity to a unit.

Question 2

Physical quantity

Answer 2

Anything that can be measured.

Question 3

Unit

Answer 3

Standard for measuring a physical quantity.

Question 4

Types of physical quantities?

Answer 4

Three: Fundamental, Scalar/Vector, and Derived.

Question 5

Fundamental P.Q.

Answer 5

A physical quantity that does NOT depend on any other P.Q. for its measurements.

Question 6

List the Fundamental P.Q.s

Answer 6

1. Length (m)
2. Mass (kg)
3. Time (s)
4. Temperature (K)
5. Current (A)
6. Luminosity (cd - candela)
7. Amount of substance (mol)

Question 7

Scalar/Vector P.Q.

Answer 7

Whether a physical quantity has direction or not.

Question 8

Derived P.Q.

Answer 8

A physical quantity that depends on one or more F.P.Q.s for its measurement.

Question 9

Identify three examples of Derived P.Q.s

Answer 9

1. Speed (distance / time) → m/s²
2. Area (length)² → m²
3. Volume (length)³ → m³

Question 10

Error

Answer 10

Uncertainty in a given measurement.

Question 11

Types of errors?

Answer 11

Two: Random and Systematic

Question 12

Random Error

Answer 12

Error due to limitations of instruments and human senses.

Question 13

Systematic Error

Answer 13

Error due to faulty equipment, setup, and/or methodology.

Question 14

Which type of error can be fully eliminated?

Answer 14

Systematic error

Question 15

Identify which errors align with Precision vs Accuracy

Answer 15

Random error → Precision (how reproducible is the same measurement = why multiple trials are conducted.)

Systematic error → Accuracy (how close the observed value is to the true value.)

Question 16

Types of Random errors?

Answer 16

Three: Absolute, Fractional, Percentage

Question 17

Structure of Absolute error?

Answer 17

x ± Δx (value ± absolute error)

Question 18

How is Absolute error determined?

Answer 18

Least count

Question 19

Least count

Answer 19

Smallest unit/Lowest value of the instrument

Question 20

Difference in least count between Analog and Digital instruments?

Answer 20

For digital, least count remains as it is. For analog, divide the given lowest value by 2 for the actual least count.

Question 21

Order of magnitude

Answer 21

Nearest power (approximation) of 10 when expressed in scientific notation.

Question 22

Error bars

Answer 22

Possible range of errors of the given value

Question 23

Direct proportionality

Answer 23

Constant rate of change
Linear, passes through the origin

(x/y) = k ⇒ x = ky
x₁/y₁ = x₂/y₂ = Constant

Question 24

Indirect proportionality

Answer 24

Constant rate of change
Hyperbola (downward curve that never touches x-OR-y-axis), does NOT pass through origin

x = k/y ⇒ xy = k
x₁/x₂ = y₁/y₂

Question 25

Linear relation

Answer 25

Straight line