Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics → Work, Energy and Power ↓


Gravitational and elastic potential energy


In physics, understanding the concepts of potential energy is important for understanding how objects behave under different forces and interactions. Today, we focus on two types of potential energy: gravitational potential energy and elastic potential energy. These energies are part of the broader concept of work, energy, and power in mechanics. Both types of energy are a type of stored energy. They have the potential to do work when conditions allow, and they play an integral role in mechanics.

Gravitational potential energy

Gravitational potential energy is the energy that is stored in an object because of its position relative to the Earth or another celestial body. It is the energy that an object has because of its height and the gravitational force acting on it. Imagine that you pick up a book from the ground and place it on a shelf; during this action, you are giving the book gravitational potential energy. If the book falls, this potential energy is converted into kinetic energy, the energy of motion.

The formula to calculate gravitational potential energy (U) is:

U = mgh

Here:

  • m is the mass of the object (in kilograms)
  • g is the acceleration due to gravity (normally 9.8 m/s² at the Earth's surface)
  • h is the height above the reference point (usually ground level, in metres)

For example, if you have a 2 kg textbook on a 1.5 m high table, the gravitational potential energy of the book can be calculated as:

U = mgh = 2 kg * 9.8 m/s² * 1.5 m = 29.4 Joules

Thus, the textbook has 29.4 joules of gravitational potential energy at this height.

Visualization of gravitational potential energy

Ground Level Height(H)

In the visualization above, the blue circle represents an object (such as a ball) raised to a height h above the ground. Gravitational potential energy increases as height increases.

Elastic potential energy

Elastic potential energy is energy that is stored in objects when they are stretched or compressed. Springs, rubber bands, and other flexible materials store energy that can be released as kinetic energy. This type of energy is a result of the configuration of a substance's constituent particles or molecules.

The formula for elastic potential energy (U) is given by Hooke's law, represented as:

U = 0.5 * k * x²

Here:

  • k is the spring constant (in N/m, a measure of the stiffness of a spring)
  • x is the displacement from the equilibrium position (in meters)

For example, if a spring with a spring constant of 150 N/m is compressed by 0.2 meters, the elastic potential energy stored in the spring is calculated as follows:

U = 0.5 * 150 N/m * (0.2 m)² = 3 Joules

Therefore, the compressed spring stores 3 joules of elastic potential energy.

Visualization of elastic potential energy

Displacement (x) balance

In the visualization above, a blue block represents a spring being compressed or stretched from its original equilibrium position. The change in length represents a change in displacement. The greater the compression or extension, the greater the stored elastic potential energy.

Comparison and applications

Both gravitational and elastic potential energy are fundamental in physics and have many real-world applications. Gravitational potential energy plays an important role in areas such as renewable energy (hydroelectric power), space exploration (satellite orbits), and daily life scenarios such as riding a bicycle uphill. Elastic potential energy is important in a variety of technologies, including shock absorbers in vehicles, trampolines, and various sports equipment.

For example, a roller coaster is an exciting place where these two energies interact vibrantly. As the coaster climbs to the top of the hill, it builds up gravitational potential energy. As it moves downhill, this energy is converted into kinetic energy. Elastic potential energy also comes into play if the coaster cars use springs to absorb shock during bumps.

Energy conservation

The law of conservation of energy states that energy cannot be created or destroyed, it can only be converted from one form to another. In the absence of external forces such as friction and air resistance, the total mechanical energy (sum of potential and kinetic energy) of a system remains constant. This principle is paramount to understanding potential energy.

Consider a pendulum: At its highest point, the pendulum has maximum gravitational potential energy and zero kinetic energy. As it swings downward, the gravitational potential energy turns into kinetic energy. When it reaches the lowest point, the kinetic energy is at its maximum, and the potential energy is at its lowest.

Illustration of energy conservation with a pendulum

prime base

Pendulum examples visually demonstrate how energy conversion occurs during motion. As the pendulum swings from its highest points (left and right) to its lowest, the energy transitions between kinetic and potential.

In summary, gravitational and elastic potential energies are important concepts to understand. They demonstrate how energy can be stored and converted into other forms, making work and motion possible under a variety of circumstances. These principles deepen our understanding of everyday phenomena and are essential foundations in the study of physics.


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Gravitational and elastic potential energy

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