Sciences · Topic 2.3
Newton's Laws & Waves
Explore how forces govern motion through Newton's three laws, perform F = ma calculations, understand work, power, and efficiency, and discover how waves transfer energy through the universe.
What You'll Learn
- State and explain Newton's three laws of motion with real-world examples
- Apply F = ma to calculate force, mass, and acceleration
- Calculate work done, power, and efficiency using correct formulas
- Distinguish between transverse and longitudinal waves
- Describe the electromagnetic spectrum and its applications
- Use wave equation: v = f × λ
IB Assessment Focus
Criterion A — Knowing: State Newton's laws, recall formulas, define wave properties accurately.
Criterion B — Inquiring: Design experiments to investigate forces and wave behaviour.
Criterion C — Processing: Perform multi-step F=ma, work, and power calculations; interpret data.
Criterion D — Reflecting: Evaluate real-world applications of forces and waves; discuss implications.
Key Vocabulary
| Term | Definition |
|---|---|
| Force | A push or pull that can change the shape, speed, or direction of an object; measured in Newtons (N) |
| Net (resultant) force | The overall force acting on an object when all forces are combined |
| Inertia | The tendency of an object to resist changes in its state of motion |
| Acceleration | The rate of change of velocity; measured in m/s² |
| Work | Energy transferred when a force moves an object; W = Fd; measured in Joules (J) |
| Power | The rate of doing work or transferring energy; P = W/t; measured in Watts (W) |
| Efficiency | (Useful energy output ÷ Total energy input) × 100% |
| Wave | A disturbance that transfers energy from one place to another without transferring matter |
| Frequency | The number of waves passing a point per second; measured in Hertz (Hz) |
| Wavelength | The distance from one point on a wave to the same point on the next wave (λ); measured in metres |
Sciences · Topic 2.3
Newton's Three Laws of Motion
Sir Isaac Newton's three laws describe how forces affect the motion of objects. Together, they form the foundation of classical mechanics.
Newton's First Law — The Law of Inertia
Statement
An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force.
This law is about inertia — the natural tendency of objects to resist changes in their state of motion. An object will not start, stop, speed up, slow down, or change direction unless a force makes it do so.
Real-world examples:
- Seatbelts: When a car stops suddenly, your body continues moving forward (inertia). The seatbelt provides the force to stop you.
- Tablecloth trick: When a tablecloth is pulled quickly, the plates stay in place because their inertia keeps them at rest.
- Bus stopping: Passengers lurch forward when the bus brakes suddenly because their bodies tend to continue moving.
- Spacecraft in space: Once moving, a spacecraft continues at constant velocity because there is no air resistance to slow it down.
Key Concept: An object moving at constant velocity in a straight line has a net force of zero. This does NOT mean no forces act on it — it means all forces are balanced. For example, a car at constant speed has driving force = friction/air resistance (balanced forces, zero net force).
Newton's Second Law — F = ma
Statement & Formula
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.F = ma (Force = mass × acceleration)
This law tells us:
- Greater force → greater acceleration (for the same mass). Push harder, accelerate faster.
- Greater mass → less acceleration (for the same force). A heavier object is harder to accelerate.
- The direction of acceleration is the same as the direction of the net force.
| Quantity | Symbol | Unit | Rearranged Formula |
|---|---|---|---|
| Force | F | Newtons (N) | F = ma |
| Mass | m | Kilograms (kg) | m = F / a |
| Acceleration | a | Metres per second squared (m/s²) | a = F / m |
Understanding units: 1 Newton is the force needed to accelerate a 1 kg mass by 1 m/s². So 1 N = 1 kg × 1 m/s² = 1 kg·m/s².
Newton's Third Law — Action-Reaction
Statement
For every action, there is an equal and opposite reaction. Forces always come in pairs.
When object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A. These are called action-reaction pairs.
Real-world examples:
- Walking: Your foot pushes backward on the ground (action). The ground pushes your foot forward (reaction). This is why you move forward.
- Rocket propulsion: The rocket pushes exhaust gases downward (action). The gases push the rocket upward (reaction).
- Swimming: Your hands push water backward (action). The water pushes your hands (and body) forward (reaction).
- Jumping off a boat: You push backward on the boat (action). The boat pushes you forward (reaction). The boat moves backward as you jump forward.
Critical Rule: Action and reaction forces act on different objects. They are NEVER on the same object and therefore do NOT cancel each other out. When you stand on the floor: you push down on the floor (action, on the floor), the floor pushes up on you (reaction, on you). These forces act on different objects, so they don't cancel.
Summary Comparison
| Law | Key Idea | When Net Force = 0 | When Net Force ≠ 0 |
|---|---|---|---|
| 1st | Inertia | Object stays at rest or constant velocity | Object accelerates (changes speed/direction) |
| 2nd | F = ma | a = 0 (no acceleration) | Object accelerates: a = F/m |
| 3rd | Action-Reaction | Forces always come in equal and opposite pairs acting on different objects | |
Sciences · Topic 2.3
F = ma Calculations
Practise rearranging and applying Newton's second law formula. Remember to always state the formula, substitute values, and include units in your answer.
The Formula Triangle
F = m × a m = F ÷ a a = F ÷ m
Worked Calculations
Calculation 1: Find Force
A 5 kg object accelerates at 4 m/s². Calculate the net force.
- Formula: F = ma
- Substitute: F = 5 × 4
- Answer: F = 20 N
Calculation 2: Find Acceleration
A force of 15 N acts on a mass of 3 kg. Calculate the acceleration.
- Formula: a = F / m
- Substitute: a = 15 / 3
- Answer: a = 5 m/s²
Calculation 3: Find Mass
A net force of 24 N causes an acceleration of 6 m/s². Calculate the mass of the object.
- Formula: m = F / a
- Substitute: m = 24 / 6
- Answer: m = 4 kg
Calculation 4: Multi-step (Net Force)
A 1200 kg car has a driving force of 4000 N and a friction force of 1000 N. Calculate the acceleration.
- Find net force: Fnet = 4000 - 1000 = 3000 N (forward)
- Formula: a = F / m
- Substitute: a = 3000 / 1200
- Answer: a = 2.5 m/s²
Exam Tip: Always use the net (resultant) force in F = ma, not just one of the forces. If multiple forces act on an object, find the net force first by adding forces in the same direction and subtracting opposing forces.
Weight vs Mass
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter in an object | The gravitational force acting on an object |
| Unit | Kilograms (kg) | Newtons (N) |
| Changes with location? | No (same everywhere) | Yes (depends on gravitational field strength) |
| Formula | — | W = mg (weight = mass × gravitational field strength) |
| On Earth | 70 kg | 70 × 10 = 700 N (using g = 10 m/s²) |
Sciences · Topic 2.3
Work, Power & Efficiency
Work, power, and efficiency are fundamental concepts that describe how energy is transferred and how useful that transfer is.
Work Done
Formula
W = F × d (Work = Force × distance moved in the direction of the force)
| Quantity | Unit | Symbol |
|---|---|---|
| Work | Joules (J) | W |
| Force | Newtons (N) | F |
| Distance | Metres (m) | d |
Key points:
- Work is only done when a force causes movement in the direction of the force
- If you push a wall and it doesn't move, no work is done (d = 0)
- If you carry a box horizontally, you do no work against gravity (the force is upward but movement is horizontal)
- 1 Joule = 1 Newton × 1 metre = the work done when a 1 N force moves an object 1 m
Power
Formula
P = W / t (Power = Work done ÷ time taken)
| Quantity | Unit | Symbol |
|---|---|---|
| Power | Watts (W) | P |
| Work | Joules (J) | W |
| Time | Seconds (s) | t |
- Power is the rate of doing work — how quickly energy is transferred
- 1 Watt = 1 Joule per second (1 W = 1 J/s)
- A more powerful machine does the same work in less time (or more work in the same time)
- 1 kilowatt (kW) = 1000 W 1 megawatt (MW) = 1,000,000 W
Efficiency
Formula
Efficiency = (Useful energy output ÷ Total energy input) × 100%
- Efficiency is always between 0% and 100% (it can never exceed 100%)
- No machine is 100% efficient — some energy is always lost as heat (due to friction) or sound
- The "wasted" energy is not destroyed (conservation of energy) — it is simply transferred to forms we don't want
Example: A motor uses 500 J of electrical energy to lift a box. The gravitational potential energy gained by the box is 350 J. Calculate the efficiency.
- Useful output = 350 J, Total input = 500 J
- Efficiency = (350 / 500) × 100% = 70%
- This means 30% (150 J) was wasted as heat and sound
Sciences · Topic 2.3
Waves & the Electromagnetic Spectrum
Waves transfer energy from one place to another without transferring matter. Understanding wave types and the electromagnetic spectrum is essential for modern science and technology.
Wave Properties
| Property | Definition | Unit |
|---|---|---|
| Wavelength (λ) | The distance from one point on a wave to the same point on the next wave (e.g. crest to crest) | Metres (m) |
| Frequency (f) | The number of complete waves passing a point per second | Hertz (Hz) |
| Amplitude | The maximum displacement from the rest position (related to energy/loudness) | Metres (m) |
| Wave speed (v) | How fast the wave travels | Metres per second (m/s) |
| Period (T) | The time for one complete wave to pass; T = 1/f | Seconds (s) |
The Wave Equation
Formula
v = f × λ (Wave speed = frequency × wavelength)
Rearrangements:
v = fλ f = v / λ λ = v / f
Types of Waves
| Feature | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Oscillation direction | Perpendicular (at right angles) to the direction of energy transfer | Parallel to the direction of energy transfer |
| What they look like | Crests and troughs (up-and-down pattern) | Compressions and rarefactions (push-and-pull pattern) |
| Examples | Light, water waves (surface), electromagnetic waves, waves on a string | Sound, ultrasound, seismic P-waves |
| Can travel through vacuum? | EM waves: Yes. Water waves: No. | No (need a medium to travel through) |
Key Distinction: Sound waves are longitudinal — they require a medium (solid, liquid, or gas) and CANNOT travel through a vacuum. Light (and all electromagnetic waves) are transverse — they CAN travel through a vacuum. This is why astronauts can see in space but cannot hear each other without radios.
The Electromagnetic Spectrum
The electromagnetic (EM) spectrum is the full range of electromagnetic radiation, ordered by wavelength (or frequency). All EM waves travel at the speed of light in a vacuum: approximately 3 × 10&sup8; m/s.
| Type | Wavelength | Frequency | Common Uses | Dangers |
|---|---|---|---|---|
| Radio waves | Longest | Lowest | TV, radio, communication | Generally safe |
| Microwaves | ↓ | ↓ | Cooking, mobile phones, satellites | Can heat body tissue |
| Infrared (IR) | ↓ | ↓ | Remote controls, thermal imaging, heating | Can cause burns |
| Visible light | ↓ | ↓ | Seeing, fibre optics, photography | Bright light can damage eyes |
| Ultraviolet (UV) | ↓ | ↓ | Sterilisation, fluorescence, sun tanning | Sunburn, skin cancer, eye damage |
| X-rays | ↓ | ↓ | Medical imaging (bones), airport security | Can damage cells, cause cancer |
| Gamma rays | Shortest | Highest | Cancer treatment (radiotherapy), sterilising equipment | Most dangerous; can kill cells |
Key Relationships
- As wavelength decreases, frequency increases (they are inversely proportional)
- As frequency increases, energy increases (higher frequency = more energy = more dangerous)
- All EM waves travel at the same speed in a vacuum (speed of light: 3 × 10&sup8; m/s)
- Radio waves have the longest wavelength / lowest frequency / lowest energy
- Gamma rays have the shortest wavelength / highest frequency / highest energy
Memory Aid for EM Spectrum Order
Running Mice In Venice Usually X-ray Goldfish
(Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma)
Visible Light Spectrum
Visible light is just a tiny part of the EM spectrum that human eyes can detect. It can be split into its component colours by a prism (dispersion):
Red → Orange → Yellow → Green → Blue → Indigo → Violet (ROYGBIV)
Red has the longest wavelength (lowest frequency). Violet has the shortest wavelength (highest frequency).
Sciences · Topic 2.3
Worked Examples
These examples demonstrate the structured approach expected at Grade 8. Always write the formula, substitute, calculate, and include units.
EXAMPLE 1A 1500 kg car accelerates from rest to 20 m/s in 10 seconds. Calculate the net force.
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Full Solution
Step 1: Find acceleration. a = (v - u) / t = (20 - 0) / 10 = 2 m/s²
Step 2: Apply F = ma. F = 1500 × 2 = 3000 N
The net force acting on the car is 3000 N in the direction of motion.
Step 2: Apply F = ma. F = 1500 × 2 = 3000 N
The net force acting on the car is 3000 N in the direction of motion.
EXAMPLE 2A crane lifts a 200 kg load a height of 15 m. Calculate the work done against gravity. (Use g = 10 m/s²)
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Full Solution
Step 1: Find the force (weight of the load). W = mg = 200 × 10 = 2000 N
Step 2: Calculate work done. Work = F × d = 2000 × 15 = 30,000 J (or 30 kJ)
The crane does 30,000 Joules of work against gravity to lift the load.
Step 2: Calculate work done. Work = F × d = 2000 × 15 = 30,000 J (or 30 kJ)
The crane does 30,000 Joules of work against gravity to lift the load.
EXAMPLE 3The crane in Example 2 takes 25 seconds to lift the load. Calculate the power output. Then, if the motor uses 40,000 J of electrical energy, calculate the efficiency.
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Full Solution
Power:
P = W / t = 30,000 / 25 = 1200 W (or 1.2 kW)
Efficiency:
Efficiency = (useful output / total input) × 100%
= (30,000 / 40,000) × 100%
= 75%
This means 75% of the electrical energy was converted to useful gravitational potential energy. The remaining 25% (10,000 J) was wasted as heat and sound due to friction.
P = W / t = 30,000 / 25 = 1200 W (or 1.2 kW)
Efficiency:
Efficiency = (useful output / total input) × 100%
= (30,000 / 40,000) × 100%
= 75%
This means 75% of the electrical energy was converted to useful gravitational potential energy. The remaining 25% (10,000 J) was wasted as heat and sound due to friction.
EXAMPLE 4Explain, using Newton's Third Law, why a person jumping off a small boat causes the boat to move backward.
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Full Solution
When the person jumps, they push backward and downward on the boat with their feet (this is the action force, acting on the boat).
By Newton's Third Law, the boat simultaneously pushes the person forward and upward with an equal force in the opposite direction (this is the reaction force, acting on the person).
Key points:
• The two forces are equal in magnitude and opposite in direction
• They act on different objects (action on the boat, reaction on the person)
• This is why the boat moves backward while the person moves forward
• The boat may move more noticeably than expected because it typically has less mass than the person, so it experiences greater acceleration (F = ma: same force, less mass = more acceleration).
By Newton's Third Law, the boat simultaneously pushes the person forward and upward with an equal force in the opposite direction (this is the reaction force, acting on the person).
Key points:
• The two forces are equal in magnitude and opposite in direction
• They act on different objects (action on the boat, reaction on the person)
• This is why the boat moves backward while the person moves forward
• The boat may move more noticeably than expected because it typically has less mass than the person, so it experiences greater acceleration (F = ma: same force, less mass = more acceleration).
EXAMPLE 5A wave has a frequency of 500 Hz and a wavelength of 0.66 m. Calculate the wave speed.
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Full Solution
Formula: v = f × λ
Substitute: v = 500 × 0.66
Answer: v = 330 m/s
This is approximately the speed of sound in air at room temperature, which confirms the answer is reasonable.
Substitute: v = 500 × 0.66
Answer: v = 330 m/s
This is approximately the speed of sound in air at room temperature, which confirms the answer is reasonable.
EXAMPLE 6An FM radio station broadcasts at a frequency of 100 MHz. Calculate the wavelength. (Speed of EM waves = 3 × 10&sup8; m/s)
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Full Solution
Formula: λ = v / f
Convert: 100 MHz = 100 × 10&sup6; Hz = 10&sup8; Hz
Substitute: λ = (3 × 10&sup8;) / (10&sup8;)
Answer: λ = 3 m
The wavelength is 3 metres. This makes sense — radio waves have long wavelengths.
Convert: 100 MHz = 100 × 10&sup6; Hz = 10&sup8; Hz
Substitute: λ = (3 × 10&sup8;) / (10&sup8;)
Answer: λ = 3 m
The wavelength is 3 metres. This makes sense — radio waves have long wavelengths.
Sciences · Topic 2.3
Practice Q&A
Attempt each question before revealing the model answer. Always show your working and include units.
CALCULATEA force of 15 N acts on a mass of 3 kg. Calculate the acceleration.
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Model Answer
Using Newton's 2nd Law: F = ma → a = F/m = 15/3 = 5 m/s².
The object accelerates at 5 metres per second squared in the direction of the force.
The object accelerates at 5 metres per second squared in the direction of the force.
EXPLAINExplain Newton's Third Law using the example of a rocket launching.
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Model Answer
The rocket engines push hot exhaust gases downward at high speed (action force, acting on the gases). By Newton's Third Law, the gases push the rocket upward with an equal force in the opposite direction (reaction force, acting on the rocket).
These forces are equal in magnitude and opposite in direction, but they act on different objects — one on the gases, one on the rocket. The rocket accelerates upward because the upward reaction force exceeds the rocket's weight.
These forces are equal in magnitude and opposite in direction, but they act on different objects — one on the gases, one on the rocket. The rocket accelerates upward because the upward reaction force exceeds the rocket's weight.
CALCULATEA 70 kg person climbs a 4 m staircase in 5 seconds. Calculate: (a) work done, (b) power. (g = 10 m/s²)
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Model Answer
(a) Work done:
Weight = mg = 70 × 10 = 700 N
Work = F × d = 700 × 4 = 2800 J
(b) Power:
P = W / t = 2800 / 5 = 560 W
Weight = mg = 70 × 10 = 700 N
Work = F × d = 700 × 4 = 2800 J
(b) Power:
P = W / t = 2800 / 5 = 560 W
EXPLAINA book is sitting on a table. Explain why it remains stationary using Newton's First Law.
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Model Answer
The book is at rest and remains at rest because the net force acting on it is zero (balanced forces). Two forces act on the book:
• Weight (gravity) pulling it downward
• Normal reaction force from the table pushing it upward
These two forces are equal in magnitude and opposite in direction, so they balance. By Newton's First Law, since the net force is zero, the book remains in its current state of motion (at rest).
• Weight (gravity) pulling it downward
• Normal reaction force from the table pushing it upward
These two forces are equal in magnitude and opposite in direction, so they balance. By Newton's First Law, since the net force is zero, the book remains in its current state of motion (at rest).
COMPARECompare transverse and longitudinal waves. Give an example of each.
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Model Answer
Transverse waves: The oscillations are perpendicular (at right angles) to the direction of energy transfer. They have crests and troughs. Example: light waves, water surface waves.
Longitudinal waves: The oscillations are parallel to the direction of energy transfer. They have compressions and rarefactions. Example: sound waves.
Key difference: Sound (longitudinal) requires a medium and cannot travel through a vacuum. Light (transverse EM wave) can travel through a vacuum.
Longitudinal waves: The oscillations are parallel to the direction of energy transfer. They have compressions and rarefactions. Example: sound waves.
Key difference: Sound (longitudinal) requires a medium and cannot travel through a vacuum. Light (transverse EM wave) can travel through a vacuum.
CALCULATEA lightbulb has an efficiency of 20%. If it uses 100 J of electrical energy, how much useful light energy is produced?
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Model Answer
Efficiency = (Useful output / Total input) × 100%
20% = (Useful output / 100) × 100%
Useful output = 20% × 100 = 20 J
Only 20 J is converted to useful light energy. The remaining 80 J is wasted as heat.
20% = (Useful output / 100) × 100%
Useful output = 20% × 100 = 20 J
Only 20 J is converted to useful light energy. The remaining 80 J is wasted as heat.
EXPLAINWhy are gamma rays more dangerous than radio waves?
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Model Answer
Gamma rays have a much higher frequency and shorter wavelength than radio waves. Since energy is directly proportional to frequency, gamma rays carry far more energy per photon.
This high energy allows gamma rays to penetrate deep into body tissues and ionise atoms (knock electrons off atoms), which can damage DNA and cause mutations, cell death, and cancer. Radio waves have very low energy and generally cannot damage biological tissue.
This high energy allows gamma rays to penetrate deep into body tissues and ionise atoms (knock electrons off atoms), which can damage DNA and cause mutations, cell death, and cancer. Radio waves have very low energy and generally cannot damage biological tissue.
Sciences · Review
Flashcard Review
Tap each card to reveal the answer. Try to answer from memory first.
State Newton's First Law.
An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force. (Law of Inertia)
Tap to reveal
State Newton's Second Law and its formula.
Force = mass × acceleration (F = ma). Acceleration is directly proportional to force and inversely proportional to mass. Units: N = kg × m/s².
Tap to reveal
State Newton's Third Law.
For every action, there is an equal and opposite reaction. The two forces act on DIFFERENT objects and therefore do NOT cancel out.
Tap to reveal
What is the formula for work done?
W = F × d (Work = Force × distance moved in the direction of the force). Unit: Joules (J). 1 J = 1 N × 1 m.
Tap to reveal
What is the difference between work and power?
Work = Force × distance (Joules). Power = Work ÷ time (Watts). Power measures the RATE of doing work — how quickly energy is transferred.
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How do you calculate efficiency?
Efficiency = (Useful energy output ÷ Total energy input) × 100%. It is always between 0% and 100%. Energy is never created or destroyed, just wasted.
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What is the difference between transverse and longitudinal waves?
Transverse: oscillations perpendicular to direction of travel (e.g. light). Longitudinal: oscillations parallel to direction of travel (e.g. sound).
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State the wave equation.
v = f × λ (wave speed = frequency × wavelength). v in m/s, f in Hz, λ in metres.
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List the electromagnetic spectrum in order.
Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma. (Longest wavelength to shortest; lowest frequency to highest.)
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Which EM wave has the highest energy?
Gamma rays have the highest frequency, shortest wavelength, and highest energy. They are the most dangerous and can ionise atoms, damage DNA, and cause cancer.
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What is the speed of light?
Approximately 3 × 10&sup8; m/s (300,000,000 m/s). All electromagnetic waves travel at this speed in a vacuum.
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Weight vs Mass?
Mass = amount of matter (kg), same everywhere. Weight = gravitational force (N), changes with location. W = mg (g ≈ 10 m/s² on Earth).
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Why can't sound travel through space?
Sound is a longitudinal wave that requires a medium (particles) to travel through. Space is a vacuum (no particles), so sound cannot propagate. Light (EM wave) can travel through vacuum.
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What is a net (resultant) force?
The overall combined force on an object when all forces are added together. If net force = 0, forces are balanced (no acceleration). If net force ≠ 0, the object accelerates.
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Why does a passenger lurch forward when a bus brakes?
Newton's First Law (inertia). The passenger's body tends to continue moving forward at the bus's original speed. The braking force acts on the bus, not directly on the passenger.
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Sciences · Practice Test
Practice Test — 20 Questions
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