The concept of weight as an effect of the gravitational field is fundamental in understanding dynamics and Newton's laws of motion. For students pursuing AS & A Level Physics (9702), this topic elucidates how gravitational forces influence the motion and interactions of objects. Grasping this concept is essential for comprehending more complex physical phenomena and applications in various scientific and engineering fields.

Key Concepts

Definition of Weight

Weight is defined as the force exerted on an object due to gravity. It is a vector quantity, possessing both magnitude and direction, typically directed towards the center of the gravitational source. The equation representing weight ($W$) is:

$$ W = m \cdot g $$

where:

$m$ = mass of the object (in kilograms)
$g$ = acceleration due to gravity (approximately $9.81 \, \text{m/s}^2$ on Earth's surface)

It is crucial to distinguish between mass and weight; mass is a measure of the amount of matter in an object and remains constant regardless of location, whereas weight varies depending on the gravitational field strength.

Gravitational Field

A gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. The gravitational field ($\vec{g}$) at a point in space is defined as the gravitational force per unit mass experienced by a small test mass placed at that point:

$$ \vec{g} = \frac{\vec{F}}{m} $$

Where:

$\vec{F}$ = gravitational force experienced by the test mass
$m$ = mass of the test mass

The direction of the gravitational field is always towards the mass creating the field. The strength of the field decreases with the square of the distance from the source mass, as described by Newton's law of universal gravitation.

Newton's Law of Universal Gravitation

Newton's law of universal gravitation states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is given by:

$$ F = G \cdot \frac{m_1 \cdot m_2}{r^2} $$

Where:

$F$ = gravitational force between the two masses
$G$ = gravitational constant ($6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$)
$m_1$, $m_2$ = masses of the two objects
$r$ = distance between the centers of the two masses

This law explains not only the weight of objects on Earth but also the gravitational interactions between celestial bodies.

Weight vs. Mass

Understanding the distinction between weight and mass is paramount:

Mass is a scalar quantity representing the amount of matter in an object, measured in kilograms (kg).
Weight is a vector quantity representing the gravitational force on an object, measured in newtons (N).

For example, an object with a mass of 10 kg will have a weight of approximately 98.1 N on Earth ($W = 10 \, \text{kg} \times 9.81 \, \text{m/s}^2$). However, the same mass would have a different weight on the Moon due to the Moon's weaker gravitational field.

Variation of Weight with Gravitational Field

Weight varies directly with the strength of the gravitational field. This relationship is expressed by the equation:

$$ W = m \cdot g $$

Where $g$ can change based on the celestial body or altitude. For instance:

On Earth, $g \approx 9.81 \, \text{m/s}^2$
On the Moon, $g_{\text{Moon}} \approx 1.62 \, \text{m/s}^2$
At higher altitudes above Earth, $g$ decreases as the distance from Earth's center increases.

This variability demonstrates why astronauts weigh less on the Moon and why precise calculations are necessary for space missions.

Apparent Weight

Apparent weight is the normal force exerted by a surface on an object in contact with it. It can differ from true weight when additional forces are at play, such as acceleration or deceleration. The relationship is given by:

$$ W_{\text{apparent}} = m \cdot (g \pm a) $$

Where $a$ is the acceleration. For example, an elevator accelerating upward increases the apparent weight, while one accelerating downward decreases it.

Free-Body Diagrams

Free-body diagrams are essential tools in physics for visualizing the forces acting on an object. To illustrate weight as an effect of the gravitational field:

Draw the object as a point or simple shape.
Represent the weight with an arrow pointing downward, labeled $W$ or $mg$.
Include other forces as applicable, such as normal force ($N$) or tension ($T$).

These diagrams aid in solving problems related to motion and equilibrium.

Measurement of Weight

Weight is measured using devices like scales, which respond to the normal force exerted by the gravitational field. Common types include:

Spring Scales: Measure weight based on the extension of a spring proportional to the force applied.
Balance Scales: Compare the weight of an object against known masses using a lever system.

Accurate measurement of weight is crucial in various applications, from everyday use to scientific experiments.

Impact of Altitude on Weight

As altitude increases, the distance ($r$) from the center of the Earth increases, which according to Newton's law of gravitation, decreases the gravitational force and thus weight. The relationship is given by:

$$ g = G \cdot \frac{M_{\text{Earth}}}{(R_{\text{Earth}} + h)^2} $$

Where:

$G$ = gravitational constant
$M_{\text{Earth}}$ = mass of the Earth
$R_{\text{Earth}}$ = radius of the Earth
$h$ = altitude above Earth's surface

This effect is noticeable in high-altitude locations and must be considered in engineering and aerospace applications.

Weightlessness and Microgravity

Weightlessness occurs when the gravitational forces are not felt by objects, typically in free-fall conditions. In microgravity environments, such as orbiting spacecraft, objects appear to be weightless because they are in continuous free fall towards Earth, creating a state of apparent weightlessness.

Understanding weightlessness is essential for space missions, as it affects human physiology and the behavior of fluids and objects in space.

Advanced Concepts

Mathematical Derivation of Gravitational Acceleration

To derive the expression for gravitational acceleration ($g$) at a distance ($r$) from the center of a spherical mass ($M$), we start with Newton's law of universal gravitation and Newton's second law of motion:

$$ F = G \cdot \frac{M \cdot m}{r^2} $$ $$ F = m \cdot a $$

Setting the two expressions for force equal to each other:

$$ m \cdot a = G \cdot \frac{M \cdot m}{r^2} $$

Canceling $m$ from both sides:

$$ a = G \cdot \frac{M}{r^2} $$

Thus, the gravitational acceleration is:

$$ g = G \cdot \frac{M}{r^2} $$

This derivation shows that gravitational acceleration depends on the mass of the gravitational source and inversely on the square of the distance from its center.

Potential Energy in a Gravitational Field

The gravitational potential energy ($U$) of an object in a gravitational field is given by:

$$ U = m \cdot g \cdot h $$

Where:

$m$ = mass of the object
$g$ = gravitational acceleration
$h$ = height above a reference point

Potential energy plays a critical role in dynamics, especially in scenarios involving motion under gravity, such as projectile motion and orbital mechanics.

Equilibrium Conditions

An object is in static equilibrium when the sum of all forces acting on it is zero. For an object resting on a surface:

The downward gravitational force (weight) is balanced by the upward normal force ($N$).

In dynamic equilibrium, such as an object moving at constant velocity, the forces still balance out, maintaining steady motion without acceleration.

Non-Inertial Frames and Apparent Forces

In non-inertial (accelerating) frames of reference, additional apparent forces, such as the centrifugal force or Coriolis force, must be considered. When analyzing weight in such frames, the apparent weight may differ from the true weight due to these inertial effects.

The apparent weight in an accelerating frame is given by:

$$ W_{\text{apparent}} = m \cdot (g \pm a_{\text{frame}}) $$

Where $a_{\text{frame}}$ is the acceleration of the frame. This concept is vital in understanding dynamics in rotating systems and accelerating vehicles.

Gravitational Fields in General Relativity

While Newtonian gravity provides a sufficient framework for most practical purposes, general relativity offers a more comprehensive understanding of gravitational fields. According to Einstein's theory, gravity is not merely a force but a curvature of spacetime caused by mass and energy.

In this context, weight can be interpreted as the resistance felt by an object moving along a geodesic in curved spacetime. This advanced perspective is essential for high-precision applications like GPS technology and understanding astrophysical phenomena.

Interdisciplinary Connections

The concept of weight as an effect of gravitational fields intersects with various other disciplines:

Engineering: Understanding weight is crucial in structural engineering, aerospace design, and mechanical systems to ensure stability and functionality.
Astronomy: Gravitational fields dictate orbital mechanics, the formation of celestial bodies, and the behavior of galaxies.
Biology: Research on the effects of microgravity on living organisms informs space medicine and the feasibility of long-term space travel.
Economics: The principles of gravity have been metaphorically applied in models like the gravity model of trade, which predicts bilateral trade flows based on economic sizes and distance.

These connections highlight the pervasive influence of gravitational concepts across diverse fields.

Complex Problem-Solving: Multi-Step Reasoning

Consider a scenario where an object of mass $m$ is lifted to a height $h$ on Earth and then transported to a location at altitude $h$ where the gravitational field strength is reduced. Calculate the change in weight and potential energy.

Initial weight on Earth's surface: $W_1 = m \cdot g$
Gravitational acceleration at altitude $h$: $g_h = \frac{G \cdot M_{\text{Earth}}}{(R_{\text{Earth}} + h)^2}$
Weight at altitude $h$: $W_2 = m \cdot g_h$
Change in weight: $\Delta W = W_2 - W_1$
Potential energy at altitude $h$: $U = m \cdot g \cdot h$

Solving such problems requires applying multiple principles and calculations, ensuring a comprehensive understanding of gravitational effects.

Experimental Techniques to Measure Gravitational Field Strength

Several experimental methods are employed to measure gravitational field strength:

Newton's Pendulum: Measures gravitational acceleration by analyzing the period of a pendulum.
Gravimeters: Highly sensitive instruments that detect minute variations in the gravitational field, useful in geophysics and exploration.
Satellite Observations: Satellites like the GRACE mission map Earth's gravitational field by tracking changes in distance between twin satellites.

Understanding these techniques is essential for practical applications in science and engineering.

Comparison Table

Aspect	Weight (Newtonian)	Weight (General Relativity)
Definition	Force due to gravity: $W = mg$	Resistance in curved spacetime
Dependence on Mass	Directly proportional to mass	Related to energy-momentum tensor
Gravitational Field	Vector field representing gravitational force	Geometry of spacetime curvature
Applications	Everyday physics, engineering, basic astronomy	Astrophysics, cosmology, high-precision technologies

Summary and Key Takeaways

Weight is the gravitational force acting on an object's mass.
The gravitational field strength ($g$) determines weight and varies with location.
Newton's laws provide a foundational framework for understanding weight in dynamics.
Advanced concepts link weight to potential energy, equilibrium, and general relativity.
Interdisciplinary applications highlight the broad relevance of gravitational principles.

Examiner Tip

Tips

To remember the difference between mass and weight, use the mnemonic "M for Matter, W for Weight." Always draw accurate free-body diagrams to visualize all forces acting on an object. When solving problems, double-check your units and ensure you're using the correct gravitational acceleration value for the given scenario. Practicing multi-step problems will enhance your problem-solving skills and prepare you for exam questions.

Did You Know

Did you know that astronauts on the International Space Station (ISS) experience microgravity, making them effectively weightless? This condition allows them to float freely, enabling unique experiments not possible on Earth. Additionally, the concept of weight variation with altitude was crucial in designing precise satellite orbits, ensuring their stability and functionality.

Common Mistakes

One common mistake is confusing mass with weight. Students often think that mass changes with location, but it's actually weight that varies due to different gravitational fields. Another error is neglecting the direction of forces in free-body diagrams, leading to incorrect calculations of net force. For example, incorrectly adding forces acting in opposite directions can result in wrong conclusions about an object's motion.

FAQ

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, measured in kilograms, and remains constant regardless of location. Weight is the gravitational force acting on that mass, measured in newtons, and varies with the strength of the gravitational field.

How does altitude affect an object's weight?

As altitude increases, the distance from the Earth's center grows, resulting in a weaker gravitational field. Consequently, the weight of an object decreases with higher altitude.

Can weight be zero?

Weight can effectively be zero in a state of free fall or in a microgravity environment, such as space, where objects experience apparent weightlessness.

What is apparent weight?

Apparent weight is the normal force exerted on an object by a surface, which can differ from the true weight when additional forces like acceleration are present.

How is weight measured?

Weight is measured using scales, such as spring scales that measure force based on spring extension, or balance scales that compare an object's weight to known masses.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

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Describe Weight as Effect of Gravitational Field

Introduction

Key Concepts

Definition of Weight

Gravitational Field

Newton's Law of Universal Gravitation

Weight vs. Mass

Variation of Weight with Gravitational Field

Apparent Weight

Free-Body Diagrams

Measurement of Weight

Impact of Altitude on Weight

Weightlessness and Microgravity

Advanced Concepts

Mathematical Derivation of Gravitational Acceleration

Potential Energy in a Gravitational Field

Equilibrium Conditions

Non-Inertial Frames and Apparent Forces

Gravitational Fields in General Relativity

Interdisciplinary Connections

Complex Problem-Solving: Multi-Step Reasoning

Experimental Techniques to Measure Gravitational Field Strength

Comparison Table

Summary and Key Takeaways

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