1.1 Basic physics

Question 1

What is a scaler quantity?

Answer 1

A quantity has a magnitude or size. But has no direction

Question 2

What is a vector quantity?

Answer 2

A quantity that has both magnitude and direction.

Question 3

What are some scaler quantities?

Answer 3

Density, mass, volume, area, distance, length, speed, work, energy, power, time, resistance, temperature, potential difference(V), electrical charge, pressure.

Question 4

What are some vector quantities?

Answer 4

displacement, velocity, acceleration, force, momentum, electric field strength, magnetic field strength, gravitational field strength

Question 5

How to add vectors?

Answer 5

tip to tail.

Vectors have magnitude and direction, therefore construct a right angled triangle and the hypotenuse is the magnitude of the new force. We can work out by using pythagoras theorem and to work out the angle, we use trigonometry (sin, cos, tan)

Question 6

An object has a 5N upwards force and 8N horizontal force. What’s the new force?

Answer 6

F² = 5² + 8² = 89
F = √89 = 9.4N
tanθ = opp/adj = 5/8 
θ = tan⁻¹ (5/8) = 32°

add both forces = 9.4N at an angle of 32°

Question 7

How to convert between units?

Answer 7

Get rid of the prefix that’s already there (change it to meters)

and replace it with what you want HOWEVER FLIP THE SIGN (in meters too) and add up all the powers.

Question 8

Convert 28.5mm to nm

Answer 8

28.5mm = 28.5 x 10⁻³m to
1nm = 1 x 10⁻⁹m ➡️ Flip the sign!!! = 10⁹
Add up all the powers = 28.5 x 10⁻³ x 10⁹ = 28.5 x 10⁶nm

Question 9

Convert 9600μm² to cm²

Answer 9

9600μm = 9600 x 10⁻⁶m HOWEVER the m is squared therefore need to square 10⁻⁶ too!
9600μm² = 9600 x (10⁻⁶)² = 9600 x 10⁻¹²m²
1cm = 1 x 10⁻² however flip the sign!!! and it becomes 10²
m is squared therefore need to square 10² too = (10²)² = 10⁴
9600 x 10⁻¹² x 10⁴ = 9600 x 10⁻⁸cm²

Question 10

Convert 450kgm⁻³ to kgmm⁻³

Answer 10

Both have kg so cancel each other.
so 450m⁻³ to 450mm⁻³
450m⁻³ is already in meter so it doesn’t change ( take m = 1, 1 to the power of anything is always 1)
450mm = 450 x 10⁻³ however flip the sign so 450x10³m
the unit is in m⁻³ so (450x10³)⁻³ = 450 x 10⁻⁹mm⁻³

Question 11

What are the general rules of indices?

Answer 11

a^m x a^n = a^(m+n)
e.g 10⁷ x 10² = 10⁹

a^m ÷ a^n = a^(m-n)
e.g 10⁷ ÷ 10² = 10⁵

(a^m)^n = a^(mxn)
(10⁷)² = 10¹⁴

a^n/m = m√a^n
10⁷/² = 2√10⁷

a^-m = 1/a^m
10⁻⁷ = 1/10⁷

a^0 = 1
10⁰ = 1
7⁰ = 1
5.353⁰ = 1

Question 12

What is density?

Answer 12

The density of a substance is its mass per volume

Question 13

How to calculate density?

Answer 13

density(kgm⁻³) = mass(kg) ÷ volume(m³)
kgm⁻³ = kg per m³

ρ (roe) = m/v

Question 14

How to calculate mass?

Answer 14

Mass(kg) = density(kgm⁻³) x volume(m³)

Question 15

How to calculate volume?

Answer 15

Volume(m³) = mass(kg) ÷ density(kgm⁻³)

Question 16

What is an uncertainty value?

Answer 16

An estimate of how far an experimental quantity might be from the “true value.”

Question 17

What is absolute uncertainty?

Answer 17

± The smallest measurable unit

Question 18

How to calculate the percentage of uncertainty?

Answer 18

%U = (absolute uncertainty ÷ measured value) x 100

Question 19

What is the overall uncertainty consists of?

Answer 19

Sum of all uncertainties (all dimensions)

Question 20

What is the percentage uncertainty of density of a copper with 25cm length, width and height and a mass of 0.142kg.

Answer 20

ρ = m/v, therefore we need to add up the uncertainty of m and v

Absolute uncertainty = nearest unit of measurement

uncertainty = 25mm ± 1mm (nearest measurable unit on a ruler)
%U of length = 1 / 25 x 100 = 4%
%U of width = 1 / 25 x 100 = 4%
%U of height = 1 / 25 x 100 = 4%

volume uncertainty = 4% + 4% + 4% = 12%

uncertainty of mass = 0.142kg ± 0.0001kg (nearest measurable unit on a weighing scale)
%U = 0.0001 / 0.142 x 100 = 0.07%

%U of ρ = 12% + 0.07% = 12.07%

Question 21

How to calculate the absolute uncertainty of a list of numbers

Answer 21

range ÷ 2

Question 22

what does the term percentage error mean?

Answer 22

same as uncertainty

Question 23

How to work out absolute uncertainty?

Answer 23

Absolute uncertainty = measured value x % uncertainty(HOWEVER ÷ 100, leaves as a decimal form)

Question 23

How to work out measured value?

Answer 23

Measured value = absolute uncertainty ÷ % Uncertainty