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 → Gravitational force ↓


Universal gravitation


Universal gravitation is a fundamental concept in physics that describes the force of attraction between any two masses. This force keeps planets in orbit around stars, moons in orbit around planets, and is also responsible for a variety of phenomena that occur in our daily lives, such as objects falling to the ground when dropped. The concept of universal gravitation was introduced by Sir Isaac Newton in a brief outline in the 17th century.

The law of universal gravitation

According to Newton's law of universal gravitation, 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. This can be expressed by the following formula:

F = G * (m1 * m2) / r^2

Where:

  • F is the gravitational force between the two objects.
  • G is the gravitational constant, which is approximately equal to 6.674 × 10^-11 N(m/kg)^2.
  • m1 and m2 are the masses of the two objects.
  • r is the distance between the centers of the two masses.

This formula reveals the universal nature of gravity and its ubiquitous effect in the universe. The force is always attractive and acts along the line connecting the centers of mass.

Visualization of gravitational force

Imagine two spheres representing two masses m1 and m2, placed at a distance r from each other.

R M1 M2 Gravitational attraction

The line represents the gravitational force acting between two masses. This force pulls them toward each other, and its strength is determined by the masses involved and the distance between them.

Importance of gravity

Gravity plays a vital role in the structure and behaviour of the universe. It is the force that binds matter together to form planets, stars and galaxies. Some of the major roles of gravity are as follows:

  • Orbital motion: Gravity is responsible for keeping planets in orbit around the Sun and moons in orbit around planets. For example, the Earth orbits the Sun because of the Sun's gravitational pull.
  • Tides: The gravitational pull exerted by the moon and sun on Earth's oceans causes tides. The moon's gravity is primarily responsible for the high and low tides seen on Earth.
  • Weight: The force of gravity acts on objects with mass, increasing their weight. This is why objects fall to the ground when they are dropped.

Example of weight calculation

Consider an object with a mass of 50 kg on Earth. The gravitational force acting on it can be calculated using the formula for weight:

Weight (W) = m * g

Where:

  • W is the weight of the object.
  • m is the mass of the object, in this case 50 kg.
  • g is the acceleration due to gravity on Earth, approximately 9.81 m/s^2.
W = 50 kg * 9.81 m/s^2 = 490.5 N

Therefore, the weight of the object is 490.5 N (newtons), which is the force exerted on the object by gravity.

Complex coordination in the universe

The remarkable aspect of universal gravitation is its ability to coordinate celestial bodies in the universe. While gravity pulls objects toward one another, the initial velocities and directions of these objects tend to form stable orbits rather than collisions. This coordination results in organized structures such as planetary systems, galaxies, and galaxy clusters.

Gravitational field

The gravitational field is a model used to explain how a massive body exerts an influence on the space around it, producing a force on any other body located in that field. The strength of this field is directly proportional to the mass producing it and inversely proportional to the square of the distance from its center.

Field strength (g) = G * M / r^2

Where:

  • g is the strength of the gravitational field.
  • M is the mass of the body creating the field.
  • r is the distance from the center of mass.

Example of gravitational field strength

If we want to calculate the strength of the gravitational field at the Earth's surface, we use the Earth's mass and radius:

Let's say:

  • Mass of the Earth, M = 5.972 × 10^24 kg
  • Radius of the Earth, r = 6.371 × 10^6 m
g = (6.674 × 10^-11 N(m/kg)^2 * 5.972 × 10^24 kg) / (6.371 × 10^6 m)^2

g ≈ 9.81 m/s^2, which is the familiar acceleration due to gravity at the Earth's surface.

Gravitational effects on time and space

An interesting aspect of gravity is its effect on time and space. According to Albert Einstein's theory of general relativity, massive objects such as stars and planets distort the space-time fabric around them. This curvature of space-time alters the motion of objects and the flow of time.

Mass Space-time warp

This phenomenon implies that time flows differently in places with different gravitational fields. For example, time moves slightly faster on a mountain than at sea level due to the weaker gravitational field. Understanding gravity in the realm of space-time is important for navigating space travel and detecting time.

Applications of gravitational understanding

A deeper understanding of gravity has made possible a variety of scientific and technological advancements:

  • Space Exploration: Calculating gravitational forces and fields is important for the launch, navigation, and operation of spacecraft.
  • Astronomy: Gravitational lensing, in which light from distant stars is bent around massive objects, helps astronomers study distant celestial objects in the universe.
  • Construction and Engineering: Understanding gravity is essential to design stable structures and vehicles, ensuring their balance and safety.

Gravity assist

Space missions often use a technique called a gravitational slingshot or gravity assist to gain speed and change direction by moving around planets. This method saves fuel and allows spacecraft to reach distant destinations, which would otherwise require huge amounts of energy.

Conclusion

The concept of universal gravitation transformed our understanding of motion and structure in the universe. It explained not only how objects interact with one another through the force of gravity, but also how this force governs celestial motion and maintains cosmic harmony. Gravity continues to be a field of intense study, revealing deep insights into the universe and advancing technology that relies on its fundamental principles. The universal nature of gravity affects everything that has mass, making it a cornerstone of physics.


Grade 11 → 2.1


U
username
0%
completed in Grade 11

← Prev (2)
Gravitational force
Next (2.1.1) →
Newton's law of universal gravitation

Comments 



Universal gravitation

https://www.physicsflow.com/g11/2.1?pfal=en