Motion, Forces and Energy
#### 1.1 Physical Quantities and Measurement Techniques
Measuring Quantities
Use a *ruler** to measure length. Place the object starting from the 0 mark and read the scale at eye level.
Use a *measuring cylinder** to measure volume. For an irregular object, volume = final water level - initial water level.
Use *clocks or digital timers** to measure time.
* To measure a very short time or small distance accurately, measure multiple events and find the average.
* Example: To time one swing of a pendulum, time 20 swings (e.g., 30.0 seconds) and calculate: Time for one swing = 30.0 / 20 = 1.5 seconds.
Scalar and Vector Quantities
A *scalar** quantity has only size (magnitude).
* Examples: distance, speed, time, mass, energy, temperature.
A *vector** quantity has both size and direction.
* Examples: force, weight, velocity, acceleration, momentum.
To find the *resultant** of two vectors at right angles (like two forces), use Pythagoras' theorem.
* Example: A man walks 3 km North and then 4 km East.
* Resultant displacement = √(3² + 4²) = √25 = 5 km
* Direction is North-East.
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#### 1.2 Motion
Speed and Velocity
* Speed is distance travelled per unit time.
* Equation: speed = distance / time
* v = s / t
* Velocity is speed in a given direction. It is a vector.
* Average speed = total distance travelled / total time taken
Graphing Motion
* Distance-Time Graphs:
The *gradient (slope)** of the line equals the speed.
A flat horizontal line means the object is *at rest** (speed = 0).
A straight sloping line means *constant speed**.
A curved line means *acceleration** (increasing gradient) or deceleration (decreasing gradient).
* Speed-Time Graphs:
The *gradient (slope)** of the line equals the acceleration.
The *area under the graph** equals the distance travelled.
A flat horizontal line means *constant speed** (acceleration = 0).
A straight sloping line means *constant acceleration**.
A line sloping downwards means *deceleration**.
Acceleration
* Acceleration is the change in velocity per unit time.
* Equation: acceleration = change in velocity / time taken
* a = (v - u) / t
* Deceleration is simply negative acceleration.
The *acceleration of free fall** (g) for objects near Earth is approximately 9.8 m/s².
Falling Objects
* Without air resistance: All objects fall with the same constant acceleration (9.8 m/s²).
* With air resistance:
* As an object falls, its speed increases, so air resistance increases.
* Eventually, air resistance equals the object's weight. The resultant force is zero.
Acceleration becomes zero and the object falls at a constant speed called *terminal velocity**.
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#### 1.3 Mass and Weight
* Mass is the amount of matter in an object. It is measured in kilograms (kg) and is the same everywhere.
* Weight is the force of gravity acting on a mass. It is measured in newtons (N) and changes depending on the gravitational field.
* Equation: weight = mass × gravitational field strength
* W = m × g
* On Earth, g = 9.8 N/kg.
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#### 1.4 Density
* Density is the mass per unit volume.
* Equation: density = mass / volume
* ρ = m / V
* How to find density:
* Liquid: Measure mass of empty cylinder. Pour in liquid, measure new mass and volume. Calculate.
* Regular solid: Measure mass. Measure dimensions, calculate volume (e.g., length × width × height).
* Irregular solid (sinks): Measure mass. Find volume by water displacement. Calculate.
An object will *float** in a fluid if its density is less than the density of the fluid.
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#### 1.5 Forces
Effects of Forces
Forces can change an object's *shape, speed,** or direction of motion.
* Hooke's Law: The extension of a spring is directly proportional to the force applied (until the limit of proportionality is reached).
* Equation: force = spring constant × extension
* F = k × x
* Newton's First Law: An object will remain at rest or move at constant velocity unless acted upon by a resultant force.
* Friction is a force that opposes motion. It acts between surfaces, in liquids (drag), and in gases (air resistance).
Turning Effect (Moments)
The *moment** of a force is its turning effect.
* Equation: moment = force × perpendicular distance from the pivot
* M = F × d
* Principle of Moments: For a body to be balanced, the total clockwise moment about a pivot must equal the total anticlockwise moment about the same pivot.
An object is in *equilibrium** if the resultant force is zero and the resultant moment is zero.
Centre of Gravity
The *centre of gravity** of an object is the point where its entire weight appears to act.
* You can find it for an irregular shape by:
1. Suspending it from a point and hanging a plumb line.
2. Drawing a line along the plumb line.
3. Repeating from a different point.
4. The centre of gravity is where the lines cross.
An object is *stable** if it has a low centre of gravity and a wide base.
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#### 1.6 Momentum
* Momentum is the product of mass and velocity. It is a vector.
* Equation: momentum = mass × velocity
* p = m × v
* Impulse is the change in momentum. Impulse = force × time.
* F × t = Δ(m × v)
* Principle of Conservation of Momentum: In a closed system, the total momentum before a collision equals the total momentum after.
* Example: A 1000 kg car moving at 10 m/s crashes into a stationary 1000 kg car. If they stick together, their new speed is 5 m/s.
* Momentum before = (1000 × 10) + (1000 × 0) = 10,000 kg m/s
* Momentum after = (1000 + 1000) × v = 2000v
* 2000v = 10,000
* v = 5 m/s
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#### 1.7 Energy, Work and Power
Energy
* Energy can be stored in different ways: kinetic, gravitational potential, chemical, elastic, nuclear, and thermal.
* Energy is transferred by forces (work), heating, and waves.
* Principle of Conservation of Energy: Energy cannot be created or destroyed, only transferred from one store to another.
* Kinetic Energy (Ek): Eₖ = ½ × m × v²
* Gravitational Potential Energy (Ep): Eₚ = m × g × h
Work
* Work done is equal to the energy transferred.
* Equation: work done = force × distance moved in direction of force
* W = F × d
Energy Resources
* Non-Renewable: Fossil Fuels, Nuclear. They will run out.
* Renewable: Solar, Wind, Hydroelectric, Geothermal, Tidal, Biofuel. They will not run out.
* Efficiency: No energy transfer is 100% efficient. Efficiency is the ratio of useful energy output to total energy input.
* Equation: % Efficiency = (useful energy out / total energy in) × 100%
* Or: % Efficiency = (useful power out / total power in) × 100%
Power
* Power is the rate of doing work or transferring energy.
* Equation: power = work done / time taken
* P = W / t
* Or: power = energy transferred / time taken
* P = E / t
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#### 1.8 Pressure
* Pressure is the force per unit area.
* Equation: pressure = force / area
* p = F / A
* To reduce pressure, increase the area (e.g., snowshoes). To increase pressure, decrease the area (e.g., sharp knife).
* Pressure in Liquids: Pressure increases with depth and with the density of the liquid.
* The pressure at a point in a liquid is calculated by: pressure = density × g × height
* p = ρ × g × h
* Example: The pressure 2m below the water surface (density = 1000 kg/m³) is: p = 1000 × 9.8 × 2 = 19,600 Pa.