Science - Combined (0653) | Motion, forces and energy

Physics P1: Motion, Forces and Energy – Comprehensive Study Notes

Hello future physicists! This chapter is where we explore how things move, why they stop, and what powers them. Motion, forces, and energy are fundamental concepts that explain everything from kicking a football to the orbit of the planets. Don't worry if some of the formulas look challenging—we'll break them down step-by-step using clear language and everyday examples! Let's get moving!

P1.1 Physical Quantities and Measurement Techniques

Before studying motion, we need to know how to measure the basic quantities involved: length, volume, time, and mass.

Measuring Length and Volume

• Length: Measured using rulers (for shorter distances) or tape measures (for longer distances).
• Volume:
  • For liquids or irregular solids (using displacement), we use a measuring cylinder.
  • Tip: Always read the volume at the bottom of the meniscus (the curved surface of the liquid) at eye level to avoid parallax error.

Measuring Time Intervals

We use clocks and digital timers (stop-watches) to measure time intervals.

Measuring Multiples for Accuracy:
If you need to find the measurement of a very small object (like the thickness of one sheet of paper) or a very short time interval (like the period of one pendulum swing), measuring a single one is often inaccurate.

Step-by-step for better accuracy:

1. Measure a large number of them (e.g., the thickness of 100 sheets, or the time for 20 oscillations).
2. Divide the total measurement by the number of objects or oscillations to find the average value for one.
   Example: If 20 oscillations take 24.0 s, the period (T) is \(24.0 \, \text{s} / 20 = 1.20 \, \text{s}\).

P1.2 Motion

Motion describes how an object changes its position over time.

Speed (Core)

Speed is defined as the distance travelled per unit time. It tells us how fast an object is moving.

Key Formula:
\[v = \frac{s}{t}\]
Where: \(v\) = speed (m/s or km/h), \(s\) = distance travelled (m or km), \(t\) = time taken (s or h).

We often calculate the average speed over a journey:

Average Speed Formula:
\[\text{Average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}\]

Example: If a car travels 200 km in 4 hours, the average speed is \(200 \, \text{km} / 4 \, \text{h} = 50 \, \text{km/h}\).

Acceleration (Supplement)

Acceleration (\(a\)) is the rate of change of speed (or velocity) per unit time. It tells us how quickly an object is speeding up or slowing down.

Key Formula:
\[a = \frac{\Delta v}{\Delta t}\]
Where: \(a\) = acceleration (\(\text{m/s}^2\)), \(\Delta v\) = change in speed (\(\text{m/s}\)), \(\Delta t\) = time taken (s).

• If speed is increasing, acceleration is positive.
• If speed is decreasing, this is called deceleration, which is simply a negative acceleration.

Acceleration of Free Fall ($g$) (Supplement)
Near the Earth's surface, all objects (ignoring air resistance) fall with a constant acceleration due to gravity, called $g$.

\[g \approx 9.8\, \text{m/s}^2\] This value is constant and is used in calculations involving objects falling freely.

Motion Graphs (Core & Supplement)

Graphs are essential for analysing motion. We look at two main types:

1. Distance-Time Graphs (D-T Graphs)

These graphs show how far an object has travelled over time.

• At Rest: The line is horizontal. (Distance is not changing.)
• Constant Speed: The line is a straight line with a gradient.
• Accelerating: The line is a curve getting steeper.

Calculating Speed (Core): The speed of the object is equal to the gradient (slope) of the distance-time graph line.

\[\text{Speed} = \text{Gradient} = \frac{\text{Change in distance}}{\text{Change in time}}\]

2. Speed-Time Graphs (S-T Graphs)

These graphs show how the speed of an object changes over time.

• At Rest: The line lies on the time axis (speed = 0).
• Constant Speed: The line is horizontal (speed is not changing).
• Constant Acceleration: The line is a straight line with a positive gradient.
• Constant Deceleration: The line is a straight line with a negative gradient.

Calculating Acceleration (Supplement): The acceleration of the object is equal to the gradient (slope) of the speed-time graph line.

\[\text{Acceleration} = \text{Gradient} = \frac{\text{Change in speed}}{\text{Change in time}} = \frac{\Delta v}{\Delta t}\]

Calculating Distance Travelled (Supplement): The total distance travelled is equal to the area under the speed-time graph. This is usually calculated by dividing the area into simple shapes like rectangles (for constant speed) and triangles (for constant acceleration).

P1.3 Mass and Weight

Mass (Core)

Mass (\(m\)) is a measure of the quantity of matter contained in an object.

• Unit: kilograms (kg).
• Mass is constant regardless of location (e.g., on Earth or the Moon).

Weight (Core & Supplement)

Weight (\(W\)) is the gravitational force exerted on an object due to its mass. It is the effect of a gravitational field on that mass.

• Unit: Newtons (N).
• Weight changes depending on the gravitational field strength (g).

Gravitational Field Strength (\(g\)):

The gravitational field strength is the gravitational force per unit mass.

Key Formula:
\[g = \frac{W}{m}\]

On Earth, the gravitational field strength \(g\) is approximately:

\[g \approx 9.8\, \text{N/kg}\]

Did you know? Because \(g\) (gravitational field strength, N/kg) is equivalent to $a$ (acceleration of free fall, m/s²), the formula \(W = mg\) (Weight = mass × g) is actually a specific application of Newton's Second Law, \(F = ma\)!

P1.4 Density

Density (\(\rho\)) is defined as mass per unit volume. It tells us how tightly packed the matter in an object is.

Key Formula:
\[\rho = \frac{m}{V}\]
Where: \(\rho\) = density (\(\text{kg/m}^3\) or \(\text{g/cm}^3\)), \(m\) = mass (kg or g), \(V\) = volume (\(\text{m}^3\) or \(\text{cm}^3\)).

How to Determine Density (Core)

1. Liquid or Regularly Shaped Solid:

1. Measure the mass (\(m\)) using a balance.
2. Measure the volume (\(V\)) (using a measuring cylinder for liquids, or a ruler for regular solids).
3. Calculate density using \(\rho = m/V\).

2. Irregularly Shaped Solid (using displacement):

1. Measure the mass (\(m\)) using a balance.
2. Fill a measuring cylinder partially with water and record the initial volume (\(V_1\)).
3. Carefully submerge the solid completely. Record the final volume (\(V_2\)).
4. The volume of the solid is the difference: \(V = V_2 - V_1\).
5. Calculate density using \(\rho = m/V\).

Floating and Sinking:
Whether an object floats or sinks in a liquid depends entirely on its density compared to the liquid’s density:

• If the object's density is less than the liquid's density, it floats. (e.g., wood in water)
• If the object's density is greater than the liquid's density, it sinks. (e.g., iron in water)

P1.5 Forces

A force is a push or a pull. Forces are vectors, meaning they have both magnitude (size) and direction.

P1.5.1 Effects of Forces (Core)

A force can cause an object to change its:

1. Size or Shape: Stretching, compressing, or bending.
2. Motion: Starting, stopping, speeding up (accelerating), slowing down (decelerating), or changing direction.

Resultant Force

The resultant force is the single force that represents the combined effect of all the forces acting on an object.

• If two or more forces act along the same straight line, you find the resultant force by adding forces in one direction and subtracting forces in the opposite direction.
• Example: If you push a box with 10 N right and your friend pushes with 5 N right, the resultant force is 15 N right. If your friend pushes 5 N left, the resultant is 5 N right.

Friction and Drag

Friction (or Drag) is a force that opposes (impedes) motion between two surfaces or between an object and a fluid (liquid or gas).

• Friction converts kinetic energy into thermal energy (heating).
• Friction in a liquid is called drag (e.g., water resistance).
• Friction in a gas is called drag or air resistance (e.g., objects falling through the air).

Newton's First Law (Core)

This law describes what happens when the resultant force is zero.

If there is no resultant force on an object, the object will either:

1. Remain at rest (if it was already stationary).
2. Continue moving in a straight line at a constant speed (if it was already moving).

Newton's Second Law (Supplement)

This law describes what happens when there is a resultant force.

When a resultant force acts on an object, the object accelerates, and the acceleration is proportional to the resultant force and inversely proportional to the mass.

Key Formula:
\[F = ma\]
Where: \(F\) = resultant force (N), \(m\) = mass (kg), \(a\) = acceleration (\(\text{m/s}^2\)).

The resultant force and the acceleration are always in the same direction.

P1.6 Energy, Work and Power

Energy is the ability to do work.

P1.6.1 Energy Stores and Transfer (Core)

Energy is never created or destroyed, only transferred from one store to another or converted into different forms (Principle of Conservation of Energy).

Key Energy Stores:

• Kinetic (E_k): Energy of movement.
• Gravitational Potential (E_p): Energy stored due to height in a gravitational field.
• Chemical: Energy stored in chemical bonds (e.g., food, fuels).
• Elastic (Strain): Energy stored when an object is stretched or compressed (e.g., a coiled spring).
• Nuclear: Energy stored in the nucleus of an atom.
• Electrostatic: Energy due to charged objects.
• Internal (Thermal): Energy stored due to the motion and position of particles (heat energy).

How Energy is Transferred:

• By forces: Mechanical work done (e.g., lifting a box).
• By electrical currents: Electrical work done (e.g., powering a lamp).
• By heating: Energy flow due to temperature difference (e.g., radiator heating a room).
• By waves: (e.g., light waves from the Sun, sound waves).

Conservation of Energy (Core)
The total energy in a closed system remains constant. Energy cannot be created or destroyed, only converted from one form to another.

Analogy: Imagine energy as money. You can change your money from pounds to euros (conversion/transfer), but the total value remains the same.

P1.6.2 Work and Energy Equations (Supplement)

Work Done (\(W\))
Mechanical or electrical work done is simply the energy transferred (\(\Delta E\)).

Mechanical Work Formula (Core):
\[W = Fd = \Delta E\]
Where: \(W\) = work done (J), \(F\) = force applied (N), \(d\) = distance moved in the direction of the force (m).

Kinetic Energy (E_k) (Supplement):
\[E_k = \frac{1}{2}mv^2\]
Where: \(E_k\) = kinetic energy (J), \(m\) = mass (kg), \(v\) = speed (\(\text{m/s}\)).

Gravitational Potential Energy Change ($\Delta E_p$) (Supplement):
\[\Delta E_p = mg\Delta h\]
Where: \(\Delta E_p\) = change in GPE (J), \(m\) = mass (kg), \(g\) = gravitational field strength (\(\text{N/kg}\)), \(\Delta h\) = change in vertical height (m).

P1.6.3 Energy Resources (Core & Supplement)

The Sun is the main source of energy for almost all resources, except for geothermal (heat from Earth's core), nuclear (fission of heavy atoms), and tidal (gravitational pull of the Moon and Sun).

Common Energy Resources and Conversion:

• Fossil Fuels (Coal, Gas, Oil) & Biofuels: Chemical energy $\rightarrow$ Boiler heats water $\rightarrow$ Steam turns a turbine $\rightarrow$ Turbine turns a generator $\rightarrow$ Electrical energy.
• Nuclear Fission (Supplement): Energy released by splitting large atoms (fission) $\rightarrow$ Heat $\rightarrow$ Turbine $\rightarrow$ Generator.
• Hydroelectric/Tidal/Wind: Kinetic energy of moving water/air $\rightarrow$ Turbine $\rightarrow$ Generator $\rightarrow$ Electrical energy.
• Solar (Thermal Collectors): Infrared radiation heats water directly.
• Solar (Solar Cells/Photovoltaic): Light energy $\rightarrow$ Electrical energy directly.
• Geothermal: Internal (thermal) energy from underground $\rightarrow$ Steam $\rightarrow$ Turbine $\rightarrow$ Generator.

Efficiency of Energy Transfer (Core & Supplement)

Efficiency is a measure of how much of the total energy input is converted into useful energy output.

Efficiency Formula:

(a) Using Energy: \[\text{Efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%\]

(b) Using Power: \[\text{Efficiency} = \frac{\text{useful power output}}{\text{total power input}} \times 100\%\]

Don't worry if the calculation seems tricky! The key is always to identify the useful energy (what you want) and the total energy (what you put in). The rest is usually wasted (often as heat or sound).

P1.6.4 Power

Power (\(P\)) is defined as the work done per unit time, or the energy transferred per unit time. It measures how fast energy is used or transferred.

Key Formulas:
\[P = \frac{W}{t}\] OR \[P = \frac{\Delta E}{t}\]
Where: \(P\) = power (W, Watts), \(W\) = work done (J), \(\Delta E\) = energy transferred (J), \(t\) = time taken (s).

Electrical Power Formula (Core):
\[P = IV\]
Where: \(P\) = power (W), \(I\) = current (A), \(V\) = voltage (V).

Electrical Energy Formula (Core):
Since \(E = P \times t\), substituting \(P = IV\) gives:
\[E = IVt\]

The Kilowatt-hour (kWh) (Core):
The kilowatt-hour (kWh) is the commercial unit used by electricity companies to calculate the cost of electricity. One kWh is the energy used by a 1 kW appliance running for 1 hour.

Calculating Cost:
\[\text{Cost} = \text{Energy used (in kWh)} \times \text{Cost per kWh}\]

P1.7 Pressure

Pressure is experienced when a force is applied over an area.

Definition of Pressure (Core)

Pressure (\(p\)) is defined as the force per unit area.

Key Formula:
\[p = \frac{F}{A}\]
Where: \(p\) = pressure (\(\text{N/m}^2\) or Pa), \(F\) = force applied perpendicularly (N), \(A\) = area over which the force is distributed (\(\text{m}^2\)).

Everyday Context (Core)

The formula \(p = F/A\) shows that pressure depends on two things:

1. Force: The greater the force, the greater the pressure (if area is constant).
2. Area: The smaller the area, the greater the pressure (if force is constant).

Analogy: Why do snowshoes stop you sinking?
When you wear snowshoes, the total force (your weight, \(F\)) remains the same. However, the snowshoe greatly increases the area (\(A\)) touching the snow. This results in a much lower pressure (\(p\)), preventing you from sinking!