Conservation of Momentum
Key Idea: When no external forces act on a system, the total momentum of the system remains constant.
- Example: When a bullet is fired from a gun, the bullet and gun have equal and opposite momenta. Total momentum before and after firing is zero.
- Formula: For two colliding bodies A and B: \[ \mathbf{P’_A} + \mathbf{P’_B} = \mathbf{P_A} + \mathbf{P_B} \] This holds true for both elastic and inelastic collisions.
Impulse in Collisions
Key Idea: Impulse equals the change in momentum and determines the force direction during collisions.
- Example: A billiard ball hitting a wall:
- Case (a): Ball moves perpendicular to the wall. Impulse = \(-2mu\) (along negative x-direction).
- Case (b): Ball strikes at \(30^\circ\). Only the x-component of momentum changes. Impulse = \(-2mu \cos 30^\circ\).
- Impulse ratio (Case a : Case b) = \(\frac{2mu}{2mu \cos 30^\circ} = \frac{2}{\sqrt{3}} \approx 1.2\).
Equilibrium of a Particle
Key Idea: A particle is in equilibrium if the net external force acting on it is zero.
- For two forces: \(\mathbf{F_1} = -\mathbf{F_2}\).
- For three forces: \(\mathbf{F_1} + \mathbf{F_2} + \mathbf{F_3} = 0\). These forces form a closed triangle when drawn tip-to-tail.
- Example: A 6 kg mass hangs from a rope. A 50 N horizontal force at the midpoint creates equilibrium. The angle with the vertical depends on balancing tension and applied force (solve using component equations).
Important Concepts for NEET
- Conservation of Momentum: Total momentum of an isolated system remains constant (e.g., collisions, explosions).
- Impulse and Force Direction: Impulse is normal to the wall in collisions, regardless of impact angle.
- Equilibrium Conditions: Net force = 0. Critical for solving tension/force problems in statics.
- Elastic vs. Inelastic Collisions: Both conserve momentum; only elastic collisions conserve kinetic energy.
