### Notes from Toppers

**Detailed Notes from Toppers on “Forces On Bodies - Procedure To Solve Problems”**

**Reference: [Physics NCERT - Class 11th][1], [Class 12th][2], [HCV for Physics][3]**

**Types of Forces:**

**Gravitational force**: Acts between any two masses. Formula: (F = \frac{Gm_1m_2}{r^2}), where G is the gravitational constant, (m_1) and (m_2) are the masses of the two objects, and (r) is the distance between them.**Electromagnetic force**: Acts between charged particles. Formula: (F = k\frac{q_1q_2}{r^2}), where (k) is the Coulomb’s constant, (q_1) and (q_2) are the charges of the two particles, and (r) is the distance between them.**Nuclear force**: Acts between nucleons (protons and neutrons) in an atom’s nucleus. It is the strongest force in nature but only acts over very short distances.**Frictional force**: Opposes the relative motion of two surfaces in contact. Formula: (F = \mu N), where (\mu) is the coefficient of friction and (N) is the normal force.**Air resistance**: Acts on objects moving through a fluid (liquid or gas). Formula: (F = \frac{1}{2}\rho v^2 A), where (\rho) is the density of the fluid, (v) is the velocity of the object, and (A) is the cross-sectional area of the object.**Spring force**: Acts when a spring is stretched or compressed. Formula: (F = -kx), where (k) is the spring constant and (x) is the displacement of the spring from its original length.

**Newton’s Laws of Motion:**

**Newton’s first law of motion (Law of inertia)**: An object at rest remains at rest, and an object in motion remains in motion at a constant velocity unless acted upon by an external force.

**Newton’s second law of motion (Law of acceleration)**: The rate of change of momentum of an object is directly proportional to the net force applied to the object and inversely proportional to its mass. In equation form, it is expressed as (\sum F = ma), where (F) is the net force, (m) is the mass of the object, and (a) is the acceleration produced in the object.

**Newton’s third law of motion (Law of action and reaction)**: For every action, there is an equal and opposite reaction. In other words, whenever one object exerts a force on a second object, the second object exerts a force of equal magnitude but opposite direction on the first object.

**Equilibrium of Forces:**

**Conditions for equilibrium**: Three conditions for equilibrium are that the net force is zero, the net torque is zero, and the center of gravity of the system is directly above the base of support.**Types of equilibrium**: Stable equilibrium: A body that is in stable equilibrium will return to its original position after a small displacement. Unstable equilibrium: A body that is in unstable equilibrium will not return to its original position after a small displacement. Neutral equilibrium: A body that is in neutral equilibrium will remain in the same position after a small displacement.

**Problem Solving Techniques:**

**Free body diagrams**: A free body diagram shows all the forces acting on an object. It is drawn by imagining the object cut out of its surroundings and all the forces acting on it are shown acting on the object.**Equations of motion**: The equations of motion are three equations that describe the motion of an object. They are derived from Newton’s second law of motion.**Work-energy theorem**: The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy.**Impulse-momentum theorem**: The impulse-momentum theorem states that the net impulse on an object is equal to its change in momentum.**Conservation of energy**: The conservation of energy states that the total energy of a closed system remains constant.

**Applications of Forces:**

**Motion of objects under gravity**: Objects in free fall accelerate at a constant rate of 9.8 m/s². Projectile motion is the motion of an object that is launched into the air.**Uniform circular motion**: Uniform circular motion is the motion of an object that moves along a circular path at a constant speed.**Simple harmonic motion**: Simple harmonic motion is the motion of an object that moves back and forth along a straight line between two fixed points.**Hooke’s law**: Hooke’s law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its original length.**Fluid mechanics**: Fluid mechanics is the study of the behavior of fluids. It includes the study of water waves, ocean currents, and weather.**Thermodynamics**: Thermodynamics is the study of heat and its relation to other forms of energy.

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