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Physics

Forces

Gravitational Force Between Spherically Symmetric Bodies

Class 11
⚡ Quick Summary
If you have two round objects (like planets or even balls), the gravitational force between them acts as if all their mass is concentrated at their centers. So, you can calculate the force using the distance between their centers.
F = G * m1 * m2 / r^2
The gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is G * m1 * m2 / r^2, where r is the distance between the centres of the two bodies.

Gravitational Force on Small Bodies by the Earth (Gravity)

Class 11
⚡ Quick Summary
Gravity is just the Earth pulling things towards its center! The force of gravity on something small near the Earth's surface is approximately mg, where g is the acceleration due to gravity.
F = G * M * m / R^2, F = mg, g = G * M / R^2 (approximately 9.8 m/s^2)
  • The force of attraction exerted by the earth on other objects is called gravity.
  • Assuming the earth is spherically symmetric, the force it exerts on a particle of mass m kept near its surface is F = G * M * m / R^2, where M is the mass of the earth and R is the radius of the earth.
  • The direction of this force is towards the centre of the earth, which is called the vertically downward direction.

Electromagnetic (EM) Force - Coulomb's Law

Class 11
⚡ Quick Summary
Charged particles attract or repel each other. Like charges repel, opposite charges attract. The stronger the charges, and the closer they are, the stronger the force!
F = (1 / 4 * pi * epsilon_0) * q1 * q2 / r^2
  • If two particles having charges q1 and q2 are at rest with respect to the observer, the force between them has a magnitude F = (1 / 4 * pi * epsilon_0) * q1 * q2 / r^2 where epsilon_0 is a constant.
  • This is called Coulomb force and it acts along the line joining the particles.
  • If q1 and q2 are of the same nature (both positive or both negative), the force is repulsive; otherwise, it is attractive.

Electromagnetic Force vs. Gravitational Force

Class 11
⚡ Quick Summary
Gravity is always attractive, but it's weak compared to the electromagnetic force. The electromagnetic force between everyday objects is usually close to zero because of almost perfect charge neutrality.
N/A
  • The gravitational force between a block and the Earth is significant (e.g., 98 N for a 1 kg block 100 m above the Earth).
  • The electromagnetic force between the Earth and the block is almost zero, despite both containing many charged particles (electrons and protons).

Nuclear Forces

Class 11
⚡ Quick Summary
Nuclear forces are super strong but only work at super short distances inside the nucleus of an atom. They hold protons and neutrons together, overcoming the electrical repulsion between protons.
N/A
  • Nuclear forces act between protons, neutrons, or both.
  • They are primarily attractive.
  • They are short-ranged (effective only at distances around 10-14 m or less).
  • At very small separations (≈ 10-15 m), nuclear force is much stronger than the Coulomb force.
  • Nuclear forces are responsible for the stability of the nucleus.
  • Phenomena like radioactivity and nuclear energy (fission and fusion) result from nuclear forces.

Weak Forces

Class 11
⚡ Quick Summary
Weak forces cause changes inside particles, like when a neutron turns into a proton. They have a tiny range, even smaller than a proton.
N/A
  • Weak forces are involved in reactions involving protons, electrons, and neutrons.
  • Examples include beta decay (neutron changing into a proton, electron, and antineutrino) and positron emission (proton changing into a neutron, positron, and neutrino).
  • The range of weak forces is very small, even smaller than the size of a proton or neutron.

Scope of Classical Physics

Class 11
⚡ Quick Summary
Classical physics uses simple laws to describe things we can see, like planets, raindrops, and grains of sand. It doesn't work so well for tiny particles like atoms.
N/A
  • Classical physics is based on Newton’s laws of motion, Newton’s law of gravitation, Maxwell’s electromagnetism, Laws of thermodynamics, and the Lorentz force.
  • It accurately describes the behavior of bodies larger than 10-6 m.
  • It is applicable to heavenly bodies (sun, earth, moon) and everyday objects (grains of sand, raindrops).
  • It is not adequate for describing the behavior of subatomic particles.

Gravitational Force

Class 11
⚡ Quick Summary
Everything pulls on everything else! The bigger things are, and the closer they are, the stronger the pull.
F = G * (m1 * m2) / r^2, where G is the gravitational constant (6.67 x 10^-11 N-m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
  • Gravitational force is a fundamental force of attraction between any two objects with mass.
  • The magnitude of gravitational force depends on the masses of the objects and the distance between them.

Coulomb Force (Electric Force)

Class 11
⚡ Quick Summary
Opposites attract, like charges repel! The more charge something has, and the closer they are, the stronger the push or pull.
F = k * (q1 * q2) / r^2, where k is Coulomb's constant (approximately 9 x 10^9 N-m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
  • Coulomb force is the electric force between charged objects.
  • It can be attractive (opposite charges) or repulsive (like charges).
  • The magnitude of Coulomb force depends on the amount of charge and the distance between them.

Normal Force

Class 11
⚡ Quick Summary
Normal force is the force exerted by a surface that is supporting something's weight and is always perpendicular to the surface.
N = mg (when on a horizontal surface and no other vertical forces are acting), where m is mass, and g is acceleration due to gravity.
  • The normal force is a contact force.
  • It acts perpendicular to the surface of contact.
  • Its magnitude is often equal to the component of the weight acting perpendicular to the surface.

Frictional Force

Class 11
⚡ Quick Summary
Friction is a force that opposes motion between surfaces in contact. The rougher the surfaces, the greater the friction.
F_friction <= μN, where μ is the coefficient of friction (static or kinetic) and N is the normal force.
  • Friction is a contact force that opposes motion (or intended motion) between surfaces.
  • There are different types of friction (static, kinetic).
  • Friction depends on the nature of the surfaces and the normal force.

Spring Constant

Class 11
⚡ Quick Summary
Spring constant (k) measures how stiff a spring is. A large 'k' means it's hard to stretch or compress.
F = -kx, where F is the restoring force exerted by the spring, k is the spring constant, and x is the displacement from the spring's equilibrium position. The negative sign indicates that the force is in the opposite direction to the displacement.
  • The spring constant (k) is a measure of the stiffness of a spring.
  • It relates the force required to stretch or compress the spring to the amount of displacement.

Weight

Class 11
⚡ Quick Summary
Weight is the force of gravity pulling down on something.
W = mg, where W is weight, m is mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth's surface).
  • Weight is the force exerted on an object due to gravity.
  • Weight is a vector quantity, with direction towards the center of the Earth (or whatever celestial body is causing the gravity).

Tension in a String/Rope

11
⚡ Quick Summary
Imagine pulling on a rope. The rope pulls back on your hand. That pulling force inside the rope is called tension. It acts along the rope.
  • Tension is the force transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.
  • Tension is directed along the length of the string and pulls equally on the objects on either end.
  • For a massless string, the tension is uniform throughout the string.