Subtopics - Work, Energy, Power and Collision (NEET)
From W = Fs cosθ to collision formulas and vertical loops — master scalar energy methods
1) Work and Work-Energy Theorem
Defines work as the dot product of force and displacement (W = F·s cosθ), covers positive, negative and zero work, variable force work via integration, and proves the work-energy theorem W_net = ΔKE = ½mv² − ½mu².
2) Energy Types and Conservation
Covers kinetic energy KE = ½mv² = P²/2m, gravitational PE = mgh, elastic PE = ½kx², and the law of conservation of mechanical energy. Relates momentum and kinetic energy (P = √(2mE)).
3) Power and Collisions
Power P = dW/dt = F·v (instantaneous) or P_avg = W/t. Collision types: elastic (e = 1, KE conserved), perfectly inelastic (e = 0, bodies merge), inelastic (0 < e < 1). Elastic 1D formulas: v1 = (m1−m2)u1/(m1+m2) + 2m2u2/(m1+m2); key special cases; loss in KE for perfectly inelastic = ½·m1m2/(m1+m2)·(u1−u2)².
4) Vertical Circular Motion
Motion in a vertical loop: velocity and tension vary with position. Critical conditions: minimum speed at top v_C = √(gl) (tension = 0); minimum speed at bottom v_A = √(5gl) to complete loop; T_bottom − T_top = 6mg. Energy conservation connects all positions.
Work, Energy, Power and Collision Download Notes & Weightage Plan
For each topic in the Work, Energy, Power and Collision chapter below, you get (2) the exact resources to download and how to use them, and (3) a simple importance & time plan so NEET students know what to do first and what to revise last.
Core concept linking force and displacement via scalar product; work-energy theorem is the fundamental tool for energy-based problem solving.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Work-energy theorem applied to stopping distance (x = mv²/2F) and block-spring problems: these are direct 1-mark scorers.
- High-risk Area: Mixing up W_by_spring (negative: −½kx²) and U_spring (positive: +½kx²). Also forgetting that centripetal force does zero work.
- Best Practice Style: Mixed numerical + conceptual MCQs; 60% computation, 40% identification of sign and conditions.
KE, gravitational PE, elastic PE and their interconversion under conservation of mechanical energy. Equilibrium analysis using PE curves.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Solving for velocity after a spring releases a block (½kx² = ½mv²) or height reached after collision using conservation — direct 1-mark problems.
- High-risk Area: Sign error in work done by spring: W_by_spring = −½kx² (spring does negative work on block when block compresses or stretches it from mean). KE can never be negative.
- Best Practice Style: Mostly numerical; assertion-reason for PE curves. Equal weight on spring-block and gravitational scenarios.
Power as rate of work; elastic and inelastic collision analysis via momentum conservation plus coefficient of restitution framework.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Equal-mass elastic collision (exchange velocities) and bullet-block perfectly inelastic collision appear almost every NEET year — learn these cold.
- High-risk Area: Forgetting that KE is not conserved in 'inelastic' (most real-world) collisions. Also sign errors when one body moves opposite to the other before collision (negative initial velocity convention).
- Best Practice Style: Mostly numerical with 4 options close in value, testing precision in v1/v2 formula. Conceptual MCQs on e=1 vs e=0 conditions.
Non-uniform circular motion under gravity; critical speed conditions, tension calculations, and energy distribution at every point of the loop.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: T_A − T_C = 6mg is a direct formula question scorer. Minimum speed to complete loop (√(5gl) at bottom) appears as a 1-mark direct question.
- High-risk Area: Confusing the speed at top (√gl) with speed at bottom (√5gl) — NEET distractors specifically exploit this. Also missing that the hemisphere detachment height is 2r/3, not r/2.
- Best Practice Style: Direct formula application numericals (60%) and conceptual condition-based MCQs (40% — which regime does the particle fall into for a given u?).
Work, Energy, Power and Collision Chapter NEET Traps & Common Mistakes (Topic-Wise)
Each subtopic below is of the Work, Energy, Power and Collision chapter and shows what NEET students usually do wrong in NEET examination, a short example of the mistake, and how NEET frames the question to trick you with close options are given below.
Mistake Snapshot (What Students Do Wrong)
- Confusing stored energy with work by spring: U_spring = +½kx² (energy stored in spring), but work done BY the spring on the block = −½kx² (spring force opposes displacement from natural length).
- Double-counting work: Students add both external agent's work AND spring's work to get ΔKE, but they are equal and opposite — W_external = +½kx² = −W_spring.
A spring (k = 200 N/m) is compressed by 0.1 m. A student claims work done by spring is +1 J. Correct: W_spring on block = −½ × 200 × 0.01 = −1 J (negative; spring pushes block in direction of release, which is opposite to compression).
How NEET Frames The Trap
Work done by spring vs potential energy stored in spring
Q. A spring of spring constant k is compressed by x from its natural length. The work done BY the spring on the block during this compression is:
A. +½kx² B. −½kx² C. kx² D. 0
Trick: Answer is −½kx² (B). The spring exerts a restoring force opposing the compression direction, so work done by the spring is negative. U = +½kx² is the elastic PE stored, not the work done by the spring.
Mistake Snapshot (What Students Do Wrong)
- Forgetting the heavy-hits-light formula: When a very heavy body (m1 >> m2) hits a stationary light body: v1 ≈ u1 (heavy barely slows down) and v2 = 2u1 (light flies off at twice the speed). Students often write v2 = u1.
- Equal mass direction confusion: If m1 = m2 and both are moving in the same direction, they exchange velocities. But if u2 = 0, then v1 = 0, v2 = u1 — the first body stops completely.
A truck (mass 1000 kg, velocity 10 m/s) elastically hits a stationary ball (mass 1 kg). Students answer v_ball = 10 m/s. Correct: v_ball = 2 × 10 = 20 m/s (light body gets almost double the incoming speed).
How NEET Frames The Trap
Special cases of elastic 1D collisions — NEET loves heavy-vs-light scenarios
Q. A ball of mass m moving with speed u makes a perfectly elastic head-on collision with a stationary ball of mass 3m. The velocity of the lighter ball after collision is:
A. u/2 (forward) B. −u/2 (backward) C. 2u/3 (backward) D. u/3 (forward)
Trick: Use v1 = (m − 3m)/(m + 3m)·u = (−2m/4m)·u = −u/2. Answer is B (−u/2, backwards). When light hits heavy stationary body, the light ball bounces back.
Mistake Snapshot (What Students Do Wrong)
- Swapping top and bottom speed: v_min at top of loop = √(gl), NOT √(5gl). v_min at bottom = √(5gl) to just complete the circle. Students regularly interchange these.
- Missing T_bottom − T_top = 6mg: This result is derived from energy conservation + tension formulas and is independent of speed. However, students recompute T at each point instead of using this elegant result.
NEET 2018 asked: a body slides from height h to just complete a vertical circle of diameter D. Students chose h = D (wrong). Answer: h = 5D/4 from energy conservation (½mv² = mgh gives v² = √(5gl) at bottom, h = 5l/2 = 5D/4).
How NEET Frames The Trap
Minimum speed and tension at top vs bottom of a vertical loop
Q. A stone of mass m is tied to a string of length l and whirled in a vertical circle. The minimum velocity at the lowest point so that the string does not go slack at the highest point is:
A. √(gl) B. √(2gl) C. √(3gl) D. √(5gl)
Trick: Answer is D — √(5gl). The critical condition is T = 0 at top, giving v_top = √(gl). From energy conservation: v_bottom² = v_top² + 4gl = gl + 4gl = 5gl, so v_bottom = √(5gl).
Mistake Snapshot (What Students Do Wrong)
- Assuming all collisions conserve KE: Only perfectly elastic collisions (e = 1) conserve kinetic energy. ALL collisions conserve momentum.
- Confusing total energy with kinetic energy: Total energy (including heat, deformation energy) is always conserved. KE is only conserved in elastic collisions.
A bullet embeds in a wooden block — KE is NOT conserved (perfectly inelastic, e = 0). Students incorrectly use KE_before = KE_after. Use momentum conservation to find v_combined, then KE_after = ½(M+m)v_combined².
How NEET Frames The Trap
Which quantity is conserved in elastic vs inelastic vs perfectly inelastic collisions?
Q. In a perfectly inelastic collision between two bodies of equal mass m, one of which is at rest, the fraction of kinetic energy lost is:
A. 0 B. 1/4 C. 1/2 D. 3/4
Trick: Answer is C (1/2). By momentum conservation: mv = 2mv_f → v_f = v/2. KE_initial = ½mv²; KE_final = ½(2m)(v/2)² = mv²/4; ΔKE = ½mv²(1 − 1/2) = mv²/4. Fraction lost = (mv²/4)/(mv²/2) = 1/2.