Physical Quantities and Units

Question 1

What is a physical quantity

Answer 1

All physical quantities consist of a numerical magnitude and a unit

To represent a physical quantity, it must contain both a numerical value and the unit in which it was measured

e.g. speed, velocity, volume

Question 2

Estimate the mass of an adult
Estimate gravitational field strength
Estimate the mass of a car
Estimate the wavelength of visible light

Answer 2

Mass of an adult = 70 kg
Gravitational field strength, g = 10 m s-2
Mass of a car = 1500 kg
Wavelength of visible light = 400 nm (violet) – 700 nm (red)

Question 3

Name all the SI base units

Answer 3

mass = kg
length = m
time = s
current = A
temperature = K
amount of substance = mol

Question 4

Derived unit of force
Derived unit of energy
Derived unit of pressure

Answer 4

The Newton (N), the unit of force, is defined by the equation:
Force = mass × acceleration
N = kg × m s–2 = kg m s–2
Therefore, the Newton (N) in SI base units is kg m s–2

The Joule (J), the unit of energy, is defined by the equation:
Energy = ½ × mass × velocity2
J = kg × (m s–1)2 = kg m2 s–2
Therefore, the Joule (J) in SI base units is kg m2 s–2

The Pascal (Pa), the unit of pressure, is defined by the equation:
Pressure = force ÷ area
Pa = N ÷ m2 = (kg m s–2) ÷ m2 = kg m–1 s–2
Therefore, the Pascal (Pa) in SI base units is kg m–1 s–2

Question 5

How to check the homogeneity of equations

Answer 5

To check the homogeneity of physical equations:
- Check the units on both sides of an equation
- Determine if they are equal
- If they do not match, the equation will need to be adjusted

Question 6

Powers of 10

Answer 6

tera = 10^12
giga = 10^9
mega = 10^6
kilo = 10^3
centi = 10^-2
milli = 10^-3
micro = 10^-6
nano = 10^-9
pico = 10^-12

Question 7

What is a scalar and vector quantity?

Answer 7

Scalar is a quantity that only has magnitude
Vector is a quantity that has magnitude and direction

Question 8

How to do the triangle method of adding vectors

Answer 8

To combine vectors using the triangle method:
Step 1: link the vectors head-to-tail
Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

Question 9

How to do the parallelogram method of adding vectors

Answer 9

Step 1: link the vectors tail-to-tail
Step 2: complete the resulting parallelogram
Step 3: the resultant vector is the diagonal of the parallelogram

Question 10

Coplanar forces

Answer 10

forces that act on the same plane

Question 11

Conditions for equilibrium in vectors

Answer 11

In equilibrium, these are closed vector right-angled triangles. The vectors, when joined together, form a closed path

Question 12

How to calculate vertical and horizontal component of vectors

Answer 12

For the horizontal component, Fx = Fcosθ
For the vertical component, Fy = Fsinθ

Question 13

True value

Answer 13

a perfect measurement which reflects quantity being measured with no errors

Question 14

Uncertainty

Answer 14

an estimate of the difference between a measurement reading and the true value

• Random and systematic errors are two types of measurement errors which lead to uncertainty

Question 15

Random error

Answer 15

Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors

This affects the precision of the measurements taken

To reduce random error: repeat measurements several times and calculate an average from them

Question 16

Systematic error

Answer 16

Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method

This type of error affects the accuracy of all readings obtained

To reduce systematic errors: instruments should be recalibrated or the technique being used should be corrected or adjusted

Question 17

Zero error

Answer 17

a type of systematic error which occurs when an instrument gives a reading when the true reading is zero

Question 18

Precision and accuracy

Answer 18

Precision: how close a measured value is to each other
Accuracy: how close a measured value is to the true value

Question 19

Absolute uncertainty

Answer 19

where uncertainty is given as a fixed quantity

Question 20

Fractional uncertainty

Answer 20

where uncertainty is given as a fraction of the measurement

Question 21

Percentage uncertainty

Answer 21

where uncertainty is given as a percentage of the measurement

percentage uncertainty = absolute / measured x 100%