Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Mechanics → Gravitational force ↓


Gravitational potential energy


Gravitational potential energy is a fascinating concept in the field of physics, especially when we explore how objects interact with the force of gravity. In simple terms, gravitational potential energy, often abbreviated as GPE, is the energy that an object possesses due to its position in a gravitational field. This energy is directly related to the height of the object above the reference point, usually the ground or the Earth's surface. To clarify this concept, we will go deep into the details and explore various scenarios where gravitational potential energy plays an important role.

Understanding gravitational potential energy

Let us begin by understanding what we mean by energy in the context of physics. Energy is the potential to do work. In the case of gravitational potential energy, it is the work done against the force of gravity to raise an object to a certain height.

Formula

The formula to calculate gravitational potential energy is:

GPE = m * g * h

Where:

  • m is the mass of the object (in kilograms)
  • g is the acceleration due to gravity (in meters per second squared, usually estimated as 9.81 m/s² on Earth)
  • h is the height of the object above the reference point (in metres)

Example

Imagine that you are picking up a book from the floor and placing it on a shelf 2 meters high. The book weighs 1 kilogram.

Using our formula, gravitational potential energy is calculated as:

GPE = m * g * h
GPE = 1 kg * 9.81 m/s² * 2 m
GPE = 19.62 Joules

From this calculation we know that when the book is placed on the shelf it has 19.62 joules of energy stored in it as gravitational potential energy.

Visualization of gravitational potential energy

To understand the concept of gravitational potential energy, consider a basketball being thrown upward. As the basketball reaches its maximum height, the energy used to lift it is completely transferred to gravitational potential energy.

Height(H) Basketball

In this illustration, the basketball at the top has maximum gravitational potential energy due to its height. As it begins to fall back toward the ground, this energy is converted into kinetic energy as it accelerates downward.

Factors affecting gravitational potential energy

There are two main factors that affect the gravitational potential energy of an object:

1. Mass of the object (m)

The heavier an object is, the more gravitational potential energy it has for a given height. This is because more force is needed to lift a heavier object against gravity. For example, lifting a two-kilogram apple onto a shelf gives twice as much gravitational potential energy as lifting a one-kilogram apple to the same height.

2. Height above the reference point (h)

As the height of an object increases, so does its gravitational potential energy. This is because the object can do more work against gravity when it is at a higher altitude. For example, an eagle sitting on a tree has more gravitational potential energy than a cat sitting on the ground because the eagle is at a higher altitude.

Practical applications of gravitational potential energy

Gravitational potential energy is an essential principle in a variety of real-world applications. Some examples include:

1. Hydroelectric dam

Hydroelectric plants use the gravitational potential energy stored in water. The water is stored at an elevation in a reservoir. When released, the gravitational potential energy is converted into kinetic energy, which then drives turbines to generate electricity.

2. Roller coaster

At the top of the roller coaster hill, the car has maximum gravitational potential energy. As it descends, this potential energy is converted into kinetic energy, allowing the car to move faster along the tracks.

3. Pendulum

Anchor

A pendulum when displaced from its rest position and released, swings back and forth, converting gravitational potential energy into kinetic energy.

Energy conservation

In an isolated system, energy is conserved. This principle is known as conservation of energy. In terms of gravitational potential energy, this means that as the height of an object increases and it gets more gravitational potential energy, this energy is converted into kinetic energy as the object falls.

Energy conversion

Consider a diver on a diving board. As they jump off the board, their gravitational potential energy is converted to kinetic energy. Just before they land in the water, almost all of their gravitational potential energy is converted to kinetic energy.

Mathematical example

Example 1

A car of mass 1500 kg stands at the top of a hill 50 m high.

GPE = m * g * h
GPE = 1500 kg * 9.81 m/s² * 50 m
GPE = 735,750 Joules

Example 2

An object of mass 250 kg is located 30 m above the ground.

GPE = m * g * h
GPE = 250 kg * 9.81 m/s² * 30 m
GPE = 73,575 Joules

Example 3

A rock climber reaches the top of a cliff 100 m above the base of the cliff. If the climber's mass is 70 kg, calculate the gravitational potential energy.

GPE = m * g * h
GPE = 70 kg * 9.81 m/s² * 100 m
GPE = 68,670 Joules

Conclusion

Gravitational potential energy is a fundamental concept that helps us understand how objects interact with gravity. By understanding how mass and height affect potential energy, we can better understand the mechanics behind many natural and engineered processes. Whether we are calculating the energy stored in a load raised to a certain height or predicting the behavior of systems, gravitational potential energy provides valuable insight. As you continue to study physics, keep in mind the importance of energy conservation and how potential energy can change and affect the motion of objects in everyday life.


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