Sciences - Co-ordinated (Double) (0654) | Motion, forces and energy

P1.1 Physical Quantities and Measurement Techniques

Measuring Basic Quantities

In physics, measurement is key. We need tools to find out "how much" and "how long."

• Length: Measured using rulers, measuring tapes, or micrometers.
• Volume: For liquids or irregular solids, we use measuring cylinders (or displacement methods).
• Time: Measured using clocks and digital timers.

If you need to measure a very small distance (like the thickness of one sheet of paper) or a very short time interval (like the period of a pendulum), you measure a multiple (many sheets or many oscillations) and then find the average value by dividing by the number of multiples measured.

Key Takeaway for P1.1:

Always choose the correct tool for measurement, and remember that vectors need direction, while scalars only need magnitude (size).

P1.2 Motion

Speed, Velocity and Acceleration

Speed is how fast an object is moving. It is the distance traveled per unit time.

$$ \text{Speed } (v) = \frac{\text{Distance travelled } (S)}{\text{Time taken } (t)} $$

\(v = S/t\)

Velocity (Supplement) is defined as speed in a given direction. Since it includes direction, velocity is a vector quantity.

Acceleration (Supplement) is the change in velocity per unit time. It tells us how quickly an object speeds up or slows down.

$$ \text{Acceleration } (a) = \frac{\text{Change in velocity } (\Delta v)}{\text{Time taken } (\Delta t)} $$

\(a = \Delta v / \Delta t\)

• Acceleration means increasing speed.
• Deceleration (Supplement) means decreasing speed, which is just a negative acceleration.

Interpreting Motion Graphs

Graphs help us visualize motion easily. You must be able to sketch, plot, and interpret two main types:

1. Distance-Time Graphs

The gradient (steepness) of a distance-time graph gives the speed.

• Horizontal Line: Speed = 0. The object is at rest.
• Straight Diagonal Line (positive slope): Constant positive gradient. The object is moving at constant speed. (The steeper the slope, the faster the speed).
• Curving Upwards: Increasing gradient. The object is accelerating (speeding up).
• Curving Downwards: Decreasing gradient. The object is decelerating (slowing down).

To calculate speed (Core), find the gradient: rise / run.

2. Speed-Time Graphs

The gradient of a speed-time graph gives the acceleration.

The area under a speed-time graph gives the distance travelled.

• Horizontal Line: Acceleration = 0. The object is moving at constant speed.
• Straight Diagonal Line (positive slope): Constant positive gradient. The object has constant acceleration.
• Straight Diagonal Line (negative slope): Constant negative gradient. The object is decelerating (constant deceleration).

To calculate distance travelled (Core), find the area of the shape under the line (rectangles and triangles).

Key Takeaway for P1.2:

Motion is described by speed, velocity (speed + direction), and acceleration. Graphs are essential tools: gradient is speed on D-T graphs, and acceleration on S-T graphs. Area under S-T graph is distance.

P1.3 Mass and Weight

Although often used interchangeably in everyday life, mass and weight are very different physical quantities.

Mass (Scalar)

• Definition: Mass is a measure of the quantity of matter in an object.
• Property: Mass remains the same everywhere (on Earth, on the Moon, or in space).
• Unit: kilogram (kg).

Weight (Vector)

• Definition: Weight is the gravitational force acting on an object due to its mass.
• Property (Supplement): Weight is the effect of a gravitational field on a mass.
• Unit: newton (N).

The relationship between weight (\(W\)) and mass (\(m\)) is given by the equation:

$$ W = m \times g $$

Where \(g\) is the gravitational field strength (GFS).

Gravitational Field Strength (\(g\)):

• Definition: The gravitational force per unit mass.
• Value: Near the Earth's surface, \(g\) is approximately \(9.8 \text{ N/kg}\).
• Equivalence (Supplement): \(g\) is numerically equivalent to the acceleration of free fall (\(9.8 \text{ m/s}^2\)).

Key Takeaway for P1.3:

Mass is constant matter; weight is the force of gravity on that mass (\(W = mg\)).

P1.4 Density

Density is a measure of how tightly packed the matter is within an object.

Density Definition and Formula

• Definition: Density (\(\rho\)) is the mass per unit volume.
• Unit: kilograms per cubic metre (\(\text{kg/m}^3\)) or grams per cubic centimetre (\(\text{g/cm}^3\)).

$$ \text{Density } (\rho) = \frac{\text{Mass } (m)}{\text{Volume } (V)} $$

\(\rho = m/V\)

Determining Density (Practical Skills)

1. Liquid: Find mass using a balance. Find volume using a measuring cylinder. Calculate density.
2. Regular Solid (e.g., cube, cylinder): Find mass using a balance. Measure dimensions (length, width, height) using a ruler to calculate volume (\(V\)). Calculate density.
3. Irregular Solid (that sinks): Find mass using a balance. Determine volume by displacement (putting the object in water in a measuring cylinder and noting the change in water level). Calculate density.

Floating and Sinking

An object will float if its density is less than the density of the liquid it is placed in. It will sink if its density is greater than the liquid's density.

Example: Wood floats in water because wood is less dense than water (\(\rho_{wood} < 1000 \text{ kg/m}^3\)).

Key Takeaway for P1.4:

Density is a measure of compactness (\(\rho = m/V\)). It determines if an object floats or sinks.

P1.5 Forces

P1.5.1 Effects of Forces and Newton's Laws

Forces are pushes or pulls (vector quantities). They can produce changes in an object's:

1. Size or Shape (e.g., squashing clay).
2. Motion (e.g., accelerating a car).

Resultant Force and Equilibrium

A resultant force is the single force that represents the net effect of two or more forces acting on an object (we usually calculate this for forces acting along the same straight line, like a tug-of-war).

• Newton's First Law: An object will remain at rest or continue moving in a straight line at constant speed unless acted upon by a resultant force.
• Equilibrium: If the resultant force is zero, the object is in equilibrium (either stationary or moving at a constant velocity).

Force and Acceleration (Supplement)

Newton's Second Law links force and motion:

$$ \text{Force } (F) = \text{Mass } (m) \times \text{Acceleration } (a) $$

\(F = ma\)

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

Friction and Drag

Friction is a force between two surfaces that impedes relative motion and converts mechanical energy into heat.

Drag is the term for friction acting on an object moving through a liquid or gas (e.g., air resistance).

Elasticity (Hooke's Law - Supplement)

When you stretch an elastic solid (like a spring), the extension (\(x\)) is proportional to the force (load, \(F\)) applied, provided you don't exceed the limit of proportionality.

• Spring Constant (\(k\)): Force per unit extension.
• Formula: \(k = F/x\) (Units: N/m).

You should be able to sketch and interpret a load-extension graph, which is a straight line through the origin up to the limit of proportionality.

P1.5.2 Turning Effect of Forces (Moments)

Forces can cause objects to rotate. This turning effect is called a moment.

• Definition: Moment is the measure of the turning effect of a force about a pivot.
• Everyday Example: Opening a door (the handle is far from the pivot/hinge for a larger moment).

$$ \text{Moment} = \text{Force} \times \text{Perpendicular distance from the pivot} $$

\(M = F \times d\)

Units: Newton-metre (Nm).

Principle of Moments (Supplement):

For an object to be in equilibrium (balanced, stationary, or constant velocity), two conditions must be met:

1. Resultant force must be zero.
2. Resultant moment must be zero.

The Principle of Moments states that for an object in equilibrium, the total clockwise moment about a pivot must equal the total anticlockwise moment about the same pivot.

P1.5.3 Centre of Gravity (COG)

The centre of gravity (COG) is the single point where the entire weight of an object appears to act.

• For regularly shaped objects (spheres, cubes), the COG is exactly at the geometric centre.

Stability: The position of the COG affects stability:

• An object is more stable if it has a low centre of gravity and a wide base.
• If the COG falls outside the base area when tilted, the object will topple.

Experiment: To find the COG of an irregular shape (plane lamina), hang it freely from three different points. Draw a vertical line (plumb line) downwards from each pivot point. The point where the three lines intersect is the COG.

Key Takeaway for P1.5:

Forces change motion (\(F=ma\)) or shape. For balance, both resultant force and resultant moment must be zero. Stability is improved by a low COG.

P1.6 Energy, Work and Power

P1.6.1 Energy Stores and Transfer

Energy is the capacity to do work. It is stored in various forms (stores):

• Kinetic (E_k): Energy of movement.
• Gravitational Potential (E_p): Energy due to height in a gravitational field.
• Chemical: Energy stored in bonds (e.g., food, fuel).
• Elastic (Strain): Energy stored in stretched or compressed objects (e.g., springs).
• Nuclear: Energy stored in the nucleus of an atom.
• Electrostatic: Energy stored due to separated charges.
• Internal (Thermal): Energy related to the temperature of an object.

Energy can be transferred between stores through:

1. Mechanical Work Done (by forces).
2. Electrical Currents (electrical work done).
3. Heating (thermal transfer).
4. Waves (sound, light, electromagnetic waves).

Principle of Conservation of Energy: Energy cannot be created or destroyed, only transferred from one store to another or transformed into different types. The total energy in a closed system remains constant.

P1.6.2 Work and Power

Work Done (\(W\)):

• Work done is understood as the energy transferred mechanically or electrically.
• When a force (\(F\)) moves an object through a distance (\(d\)) in the direction of the force, work is done.

$$ W = F d = \Delta E $$

Unit: Joule (J).

Power (\(P\)):

• Definition: Power is the rate at which work is done, or the energy transferred per unit time.
• Unit: Watt (W).

$$ P = \frac{W}{t} \quad \text{or} \quad P = \frac{\Delta E}{t} $$

P1.6.3 Energy Resources and Efficiency

The main source of energy for most processes on Earth (except geothermal, nuclear, and tidal) is radiation from the Sun.

Energy Resources (Core)

We obtain useful energy/electrical power from:

• Fossil Fuels (coal, oil, gas) - High energy density, but non-renewable and polluting.
• Biofuels - Renewable, but can require large areas of land.
• Water (Hydroelectric dams, tides, waves) - Renewable, reliable (dams/tides), but often high initial cost and environmental impact (dams).
• Geothermal - Energy from hot rocks underground; renewable, but geographically limited.
• Nuclear Fission - High energy output, low carbon, but non-renewable fuel and waste disposal challenges.
• Solar (Solar cells/thermal collectors) - Renewable, clean, but unreliable (night/cloudy days).
• Wind (Wind turbines) - Renewable, clean, but unreliable (no wind).

Note: Nuclear fission and fusion (in the Sun) both release energy (Supplement), but fission involves splitting nuclei, while fusion involves joining them.

Efficiency (Supplement)

Efficiency measures how much of the total energy input is converted into useful output energy (as opposed to wasted energy, usually heat).

$$ \text{Efficiency (Energy)} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\% $$

$$ \text{Efficiency (Power)} = \frac{\text{useful power output}}{\text{total power input}} \times 100\% $$

It is crucial that energy transfer is not 100% efficient; some energy is always transferred to internal (thermal) energy, usually into the surroundings.

Key Takeaway for P1.6:

Energy is conserved but is constantly transferred and transformed. Work is energy transferred (\(W = Fd\)), and power is the rate of energy transfer (\(P = \Delta E/t\)). We seek efficient, reliable, and sustainable energy resources.

P1.7 Pressure

Pressure is all about how a force is spread out over an area.

Definition and Formula

• Definition: Pressure (\(p\)) is the force applied perpendicular to a surface per unit area.
• Unit: Pascal (\(\text{Pa}\)) or Newton per square metre (\(\text{N/m}^2\)).

$$ \text{Pressure } (p) = \frac{\text{Force } (F)}{\text{Area } (A)} $$

\(p = F/A\)

Pressure in Everyday Examples

This formula tells us that to increase pressure, you can either increase the force or decrease the area. To decrease pressure, you increase the area.

• Example of High Pressure: A sharp knife or a nail tip has a very small area, so even a moderate force results in very high pressure, allowing it to cut or pierce easily.
• Example of Low Pressure: Tractors and snowshoes have very wide tires or bases. This increases the area, spreading the weight (force) out, and reducing the pressure so they don't sink into soft ground.

Key Takeaway for P1.7:

Pressure depends on force and area (\(p = F/A\)). Small area means high pressure; large area means low pressure.