Important NEET Exam Concepts
- Power calculation using P = F · v
- Conservation of momentum in all collisions
- Difference between elastic (energy conserved) and inelastic (energy lost) collisions
- Kinetic energy transfer in elastic collisions (fractional energy loss formulas)
- Collisions in 2D: Equal masses move at right angles (90°) after elastic collision
Power
Power tells us how fast work is done. Think of it as “work speed”:
- Average power: \( P_{av} = \frac{W}{t} \) (Work divided by total time)
- Instantaneous power: \( P = \frac{dW}{dt} \) or \( P = \mathbf{F} \cdot \mathbf{v} \) (Force multiplied by velocity at that instant)
- Units:
- Watt (W) = 1 J/s
- Horsepower (hp) = 746 W
Example (Elevator): An elevator (1800 kg total) moves up at 2 m/s against 4000 N friction. Minimum power required is:
Downward force \( F = mg + F_r = (1800 \times 10) + 4000 = 22000 \, \text{N} \)
Power \( P = F \cdot v = 22000 \times 2 = 44000 \, \text{W} \) (or 59 hp)
Collisions Basics
Collisions involve two objects hitting each other. Two important rules apply:
- Momentum is ALWAYS conserved (total before = total after)
- Kinetic energy may NOT be conserved (can turn into heat/sound)
Types of Collisions
- Elastic: Objects bounce apart. Kinetic energy conserved. Example: Billiard balls.
- Inelastic: Some energy lost. Objects may stick together or deform.
- Completely inelastic: Objects stick together after collision (maximum energy loss).
1D Collisions (Head-On)
Completely Inelastic (Sticking Together)
After collision: \( m_1v_{1i} = (m_1 + m_2)v_f \)
Final velocity: \( v_f = \frac{m_1v_{1i}}{m_1 + m_2} \)
Energy loss: \( \Delta K = \frac{1}{2} \frac{m_1m_2}{m_1 + m_2} v_{1i}^2 \)
Elastic (Bouncing Apart)
Final velocities:
\( v_{1f} = \frac{m_1 – m_2}{m_1 + m_2} v_{1i} \)
\( v_{2f} = \frac{2m_1}{m_1 + m_2} v_{1i} \)
Special cases:
- Equal masses (\( m_1 = m_2 \)): \( v_{1f} = 0 \), \( v_{2f} = v_{1i} \) (first object stops)
- Heavy target (\( m_2 \gg m_1 \)): \( v_{1f} \approx -v_{1i} \), \( v_{2f} \approx 0 \) (small object bounces back)
Energy Transfer Example (Neutron Slowing)
Fractional kinetic energy lost by neutron after elastic collision:
\( f_l = \left( \frac{m_n – m_2}{m_n + m_2} \right)^2 \)
• With deuterium (\( m_2 = 2m_n \)): 89% energy lost (\( f_l = 1/9 \))
• With carbon: 71.6% energy lost
2D Collisions (Glancing Impact)
Momentum conserved along x and y axes:
- \( m_1v_{1i} = m_1v_{1f} \cos \theta_1 + m_2v_{2f} \cos \theta_2 \)
- \( 0 = m_1v_{1f} \sin \theta_1 – m_2v_{2f} \sin \theta_2 \)
Key result for equal masses: If collision is elastic and one mass starts at rest, they move at 90° to each other after collision.
Example: Billiard balls (\( m_1 = m_2 \)) with target angle \(\theta_2 = 37^\circ\) → cue ball angle \(\theta_1 = 53^\circ\).
Summary Formulas
- Power: \( P = \mathbf{F} \cdot \mathbf{v} \)
- Momentum conservation: Total \( \mathbf{p}_{\text{initial}} = \mathbf{p}_{\text{final}} \)
- 1D elastic collision: \( v_{1f} = \frac{m_1 – m_2}{m_1 + m_2} v_{1i} \), \( v_{2f} = \frac{2m_1}{m_1 + m_2} v_{1i} \)
- Energy loss in neutron collision: \( f_l = \left( \frac{m_n – m_2}{m_n + m_2} \right)^2 \)
