Unit Synthesis + Working Scientifically Investigation
In 1583, Galileo sat in Pisa Cathedral and timed a 6-metre lamp swinging with his own pulse — discovering that the period depends only on length, not on the weight or how wide it swings.
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Q1 · Without looking at notes, write as many Unit 3 concepts as you can in 2 minutes. Which topic do you know best? Which do you need to revisit?
Q2 · A pendulum swings back and forth. List every force and energy transformation you can identify.
● Know
- Newton's 3 Laws and their applications in a variety of contexts
- All 7 energy forms and key energy transformation chains
- The pendulum as a system demonstrating KE, GPE and energy conservation
● Understand
- How forces and energy connect across the whole Physical World unit
- Why the pendulum period depends on length but NOT mass or amplitude (for small swings)
- How to plan and evaluate a fair test in Working Scientifically
● Can do
- Apply Newton's 3 Laws to multi-step scenarios (car park, acceleration, braking)
- Trace energy transformations from food to bicycle motion
- Write a hypothesis and identify variables for a pendulum investigation
Newton's Law says objects resist changes to their motion — this resistance is called . When net force is , the object is in equilibrium. Energy can never be or destroyed — only .
Drop your pen and watch it fall: gravity pulls it down (a non-contact force), air resistance pushes up (a contact force), and the net force downward makes it accelerate. Catch it in your hand and both your hand and the pen push on each other equally and in opposite directions — Newton's Third Law. You've just seen all three of Newton's Laws in a single two-second event.
| Law | Statement | Everyday example |
|---|---|---|
| First Law (Inertia) | An object stays at rest or at constant velocity unless an unbalanced (net) force acts on it. | Passenger thrown forward when car brakes suddenly — inertia keeps them moving forward. |
| Second Law | Greater net force → greater acceleration. Greater mass → less acceleration (for same force). | Pushing a heavy trolley harder = faster acceleration; a loaded trolley accelerates less. |
| Third Law (Action-Reaction) | Every force has an equal and opposite reaction force on a different object. | Rocket exhaust pushes gas backward; gas pushes rocket forward. Swimmer pushes wall backward; wall pushes swimmer forward. |
Forces in Unit 3: gravity (weight), normal force, friction, tension, applied force, air resistance. A free-body diagram (FBD) shows all forces as arrows on the object — direction and relative size matter.
Net force = sum of all forces. If arrows cancel (balanced) → net force = 0 → no acceleration (but can be moving at constant speed). If arrows don't cancel (unbalanced) → net force ≠ 0 → acceleration.
Energy is the underlying thread of the entire unit. Here's the complete summary:
- 7 forms: kinetic, gravitational PE, elastic PE, heat (thermal), light (radiant), sound, chemical, electrical.
- KE: depends on mass and speed. Speed has a SQUARED effect — double the speed = 4× the KE.
- GPE: depends on mass and height above a reference point.
- Elastic PE: stored in stretched or compressed objects (springs, rubber bands).
- Transformations: every transformation wastes some energy as heat/sound (efficiency <100%).
- Conservation: total energy before = total energy after (useful + waste).
- Resources: non-renewable (fossil fuels, nuclear) vs renewable (solar, wind, hydro, biomass). Australia transitioning to 82% renewables by 2030.
A useful synthesis example — a roller coaster:
- At the top: maximum GPE, minimum KE.
- Falling: GPE → KE (speeds up).
- At the bottom: minimum GPE, maximum KE.
- Going up again: KE → GPE (slows down).
- Each cycle: some energy lost to friction and air resistance as heat/sound → coaster cannot return to original height without a motor.
Question: What factors affect the period of a pendulum?
Students typically predict that mass and amplitude will affect the period. In reality, for small swings, only the string length matters — this is a famous example of a surprising scientific result that challenges intuition.
Variables:
- Independent variable (IV): string length — test at least 3 values (e.g. 20 cm, 40 cm, 60 cm)
- Dependent variable (DV): time for 10 complete swings (divide by 10 to get period)
- Controlled variables: mass of the bob; size of the starting swing (amplitude — keep it small, <15°); location (same gravity); same person timing
Why time 10 swings? Timing one swing introduces large percentage error. Timing 10 and dividing gives a more accurate single-swing period.
Method (4 steps):
- Set up pendulum at the first string length. Pull back to a small angle (<15°), release, and immediately start the stopwatch.
- Count 10 complete swings (left → right → left = 1 swing). Stop the clock. Record time.
- Repeat steps 1–2 twice more at the same length (3 trials). Calculate average time for 10 swings.
- Change string length to the next value. Repeat for all lengths.
Results table template:
| String length (cm) | Trial 1 (s) | Trial 2 (s) | Trial 3 (s) | Average time for 10 swings (s) | Period (s) |
|---|---|---|---|---|---|
| 20 | |||||
| 40 | |||||
| 60 |
Expected finding: Period increases as length increases. A 1-metre pendulum takes exactly 2 seconds per swing (the basis of the original mechanical clock). Neither doubling the mass of the bob nor changing the starting angle will significantly affect the period (for small angles).
Wrong: "Newton's 3rd Law means forces always cancel." Action-reaction pairs act on DIFFERENT objects — you can never add them on the same free-body diagram. The 20 N you push on a wall and the 20 N the wall pushes back on you are on different objects — they don't cancel each other.
Right: 3rd Law pairs act on different objects. Balanced forces (net force = 0) act on the SAME object and cancel. Don't confuse these two ideas.
Wrong: "Energy is lost when a pendulum slows down." Energy is not lost — it is converted to heat (air resistance) and sound. The total energy of the universe is unchanged. In everyday speech we say "lost" but in physics it is "converted to less useful forms".
Right: Energy is conserved — the pendulum's mechanical energy converts to heat and sound via air resistance and friction at the pivot. Never "lost", only transformed.
Wrong: "A heavier pendulum bob swings faster." Mass has no effect on the period (for the same string length and small amplitude). This surprises most people — it's the counterintuitive result Galileo discovered. A heavier bob is pulled harder by gravity but also has more inertia — the two effects cancel exactly.
Right: Period depends only on string length (and gravity, which is constant on Earth). Mass and amplitude (for small angles) have no effect.
Newton's 3rd Law force pairs always act on objects. A pendulum slowing down is losing energy to and sound — this is not a violation of energy . Only string affects the pendulum's period.
A pendulum swings back and forth without stopping in an ideal frictionless world. Predict: at EXACTLY which point in its swing does it have (a) maximum kinetic energy, and (b) maximum gravitational potential energy? Can it have both maxima at the same time?
How close was your prediction?
The hook at the start of this lesson told the story of Galileo watching a lamp swing in Pisa Cathedral in 1583, timing it with his own pulse. Did he discover what you predicted? The period depends only on the length of the string — not the mass of the bob or how far it swings!
Look back at your list of Unit 3 concepts from Think First — what did you miss? Which topic connects most directly to Galileo's pendulum discovery, and what will you do to strengthen your weakest area before the unit assessment?
Q1. Use Newton's Three Laws to explain what happens when a car (a) sits in a car park, (b) accelerates from 0 to 60 km/h, and (c) brakes suddenly. For each, identify which law applies and why. (5 marks)
Q2. Describe the energy transformations that occur when you eat breakfast and then ride a bike to school. Start with chemical energy in the food. (4 marks)
Q3. Plan a fair test to investigate whether the length of a pendulum string affects its period. Identify all variables and write a hypothesis. (4 marks)
Answers
▾MCQ 1
A — First Law (inertia). When the car accelerates forward, your body's inertia resists the change — your body tends to stay in its previous state (stationary) while the car seat pushes you forward. You feel pressed into the seat because the seat is applying the forward force to you. Note: the car seat's force on you and your force on the seat is also a 3rd Law pair, but the primary explanation of the sensation is 1st Law inertia.
MCQ 2
B — At the top of the swing the bob is momentarily stationary (zero velocity, therefore zero KE) but at its highest point (maximum height, therefore maximum GPE). As it swings down, GPE converts to KE.
MCQ 3
C — A bicycle has rolling friction (much less than tyre-road sliding friction in a car), no internal combustion engine (which wastes ~75% of fuel as heat), and no heavy drivetrain losses. Human muscles are about 25% efficient, but the mechanical bicycle transmission itself is ~95–98% efficient.
MCQ 4
C — A light bulb transforms electrical energy into light energy (useful) and heat energy (waste). Energy is never created (A, D are wrong) or destroyed/disappeared (B is wrong) — only transformed.
MCQ 5
C — Static friction exactly matches the applied force (up to its maximum value) when an object doesn't move. Since the box doesn't move, net force = 0, so friction = 20 N. If friction were <20 N, there would be a net force and the box would accelerate. Friction acts on both moving AND stationary objects (D is wrong).
Short Answer 1
Model answer: (a) Car in car park: First Law. The car has zero net force (balanced forces — gravity down, normal force up; no engine, friction sufficient to hold it). With zero net force it remains stationary (no change in motion). (b) Accelerating: Second Law. The engine applies a forward force greater than friction/drag, producing a net force forward. Net force → acceleration; the car speeds up. More engine force → faster acceleration. (c) Braking suddenly: First Law for passengers. The car decelerates due to braking forces (net force backward on car). Passengers have inertia — they continue moving forward unless restrained by a seatbelt. Also 3rd Law: brake pads push on disc (action), disc pushes back on pads (reaction).
Short Answer 2
Model answer: Chemical energy in food → absorbed during digestion. Chemical energy in body (muscles) → when you pedal, muscles convert chemical energy to kinetic energy of your legs. Kinetic energy of legs → transferred through pedals and chain to kinetic energy of the bicycle (wheels turning). Kinetic energy of bicycle → the bicycle moves forward (kinetic energy of whole system — bike + rider). Waste energy at each step: heat (body warmth from metabolic processes, tyre friction with road, air resistance). Some sound energy also produced by tyre noise, chain, wind.
Short Answer 3
Model answer: Hypothesis: "If the length of the pendulum string is increased, then the period will increase, because a longer pendulum travels through a larger arc and takes more time to complete each swing." IV: string length (e.g. 20 cm, 40 cm, 60 cm). DV: period of the pendulum (measured by timing 10 complete swings and dividing by 10). Controlled variables: mass of bob (keep same bob throughout); starting angle (keep <15° using a protractor); same person timing; same location. Method: Set length, release from small angle, time 10 swings, divide by 10 to get period. Repeat 3 times at each length and average. Change length and repeat.