Physics - Mechanics and Properties of Matter - How to Solve: Work, Energy & Power (Work-Energy Theorem, Conservative Forces, Power of Motors) – NEET UG Physics Guide

How to Solve: Work, Energy & Power (Work-Energy Theorem, Conservative Forces, Power of Motors) – NEET UG Physics Guide

Introduction

Mastering Work, Energy & Power unlocks 8-10 marks in NEET Physics—enough to push you into the top 1%. From calculating how much force a motor needs to lift an elevator to predicting the speed of a rollercoaster at the bottom of a drop, this topic bridges theory and real-world engineering. If you can solve these problems, you’re not just passing—you’re dominating.

WHAT YOU NEED TO KNOW FIRST

Before diving in, ensure you understand: 1. Newton’s Second Law (F = ma) – How forces cause acceleration. 2. Kinetic Energy (KE = ½mv²) & Potential Energy (PE = mgh) – The two most common forms of mechanical energy. 3. Basic Calculus (for Power = dW/dt) – Only differentiation of work with respect to time is needed.

If any of these are shaky, pause and review them first.

KEY TERMS & FORMULAS

1. Work (W)

• Definition: Work is done when a force displaces an object.
• Formula: W = F · s · cosθ
• W = Work done (Joules, J)
• F = Force applied (Newtons, N)
• s = Displacement (meters, m)
• θ = Angle between force and displacement
• MEMORISE THIS: Work is scalar (no direction), but depends on the angle.

2. Work-Energy Theorem

• Definition: The net work done on an object equals its change in kinetic energy.
• Formula: W_net = ΔKE = KE_final – KE_initial
• W_net = Net work done (J)
• ΔKE = Change in kinetic energy (J)
• MEMORISE THIS: This is your go-to equation when forces and motion are involved.

3. Conservative vs. Non-Conservative Forces

4. Power (P)

• Definition: Rate of doing work (how fast energy is transferred).
• Formulas:
• P = W / t (Average power)
  • P = Power (Watts, W)
  • W = Work done (J)
  • t = Time taken (s)
• P = F · v · cosθ (Instantaneous power when force and velocity are constant)
  • F = Force (N)
  • v = Velocity (m/s)
  • θ = Angle between force and velocity
• MEMORISE THIS: 1 Horsepower (HP) = 746 Watts.

5. Efficiency (η)

• Definition: Ratio of useful output power to input power.
• Formula: η = (Output Power / Input Power) × 100%
• MEMORISE THIS: Efficiency is always less than 100% due to energy losses.

STEP-BY-STEP METHOD

Step 1: Identify the System & Forces

• Action: Draw a free-body diagram (FBD) of the object.
• Ask: Are the forces conservative (gravity, spring) or non-conservative (friction, applied force)?

Step 2: Choose the Right Energy Approach

• If only conservative forces act: Use Conservation of Mechanical Energy (KE + PE = constant).
• If non-conservative forces act: Use Work-Energy Theorem (W_net = ΔKE) or W_non-conservative = ΔKE + ΔPE.

Step 3: Write Down Known & Unknown Quantities

• List given values (mass, velocity, height, force, time, etc.).
• Identify what you need to find (speed, work, power, efficiency).

Step 4: Apply the Correct Formula

• For work: W = F · s · cosθ
• For kinetic energy: KE = ½mv²
• For potential energy: PE = mgh (gravitational) or PE = ½kx² (spring)
• For power: P = W/t or P = F · v

Step 5: Solve for the Unknown

• Plug in values and solve algebraically.
• Check units: Ensure all units are in SI (kg, m, s, J, W).

Step 6: Verify the Answer

• Does it make sense? (e.g., Power can’t be negative, efficiency < 100%)
• Cross-check with another method (e.g., use kinematics if possible).

WORKED EXAMPLES

Example 1 – Basic (Work-Energy Theorem)

Problem: A 2 kg block slides from rest down a frictionless incline of height 5 m. What is its speed at the bottom?

Solution: 1. Identify forces: Only gravity (conservative). 2. Approach: Conservation of mechanical energy (KE + PE = constant). 3. Known:
- m = 2 kg
- h = 5 m
- g = 9.8 m/s²
- Initial speed (u) = 0 → KE_initial = 0 4. At top: PE = mgh = 2 × 9.8 × 5 = 98 J 5. At bottom: PE = 0, KE = ½mv² 6. Apply conservation:
KE_initial + PE_initial = KE_final + PE_final
0 + 98 = ½ × 2 × v² + 0
98 = v² → v = √98 ≈ 9.9 m/s

What we did and why: - Used conservation of energy because only conservative forces act. - Ignored friction (given as frictionless), so no energy loss.

Example 2 – Medium (Non-Conservative Forces)

Problem: A 1000 kg car accelerates from 10 m/s to 20 m/s over 50 m. If the engine exerts a constant force of 2000 N, what is the work done by friction?

Solution: 1. Identify forces: Engine force (non-conservative), friction (non-conservative). 2. Approach: Work-Energy Theorem (W_net = ΔKE). 3. Known:
- m = 1000 kg
- u = 10 m/s, v = 20 m/s
- s = 50 m
- F_engine = 2000 N 4. Calculate ΔKE:
ΔKE = ½mv² – ½mu² = ½ × 1000 × (20² – 10²) = 500 × 300 = 150,000 J 5. Work done by engine:
W_engine = F_engine × s = 2000 × 50 = 100,000 J 6. Net work = ΔKE:
W_net = W_engine + W_friction = 150,000
100,000 + W_friction = 150,000 → W_friction = 50,000 J
(Since friction opposes motion, W_friction = -50,000 J)

What we did and why: - Used Work-Energy Theorem because non-conservative forces (engine, friction) are involved. - Friction does negative work (opposes motion).

Example 3 – Exam-Style (Power of a Motor)

Problem: A motor lifts a 500 kg elevator at a constant speed of 2 m/s. If the motor’s efficiency is 80%, what is the input power?

Solution: 1. Identify forces: Gravity (conservative), motor force (non-conservative). 2. Approach: Power = F · v, then account for efficiency. 3. Known:
- m = 500 kg
- v = 2 m/s (constant speed → a = 0 → F_net = 0)
- g = 9.8 m/s²
- η = 80% = 0.8 4. Force needed to lift at constant speed:
F = mg = 500 × 9.8 = 4900 N 5. Output power (useful power):
P_out = F · v = 4900 × 2 = 9800 W 6. Input power (since η = P_out / P_in):
P_in = P_out / η = 9800 / 0.8 = 12,250 W

What we did and why: - At constant speed, net force = 0 → motor force = weight. - Used P = F · v for instantaneous power. - Efficiency relates input power to output power.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP (Night Before Exam)

"Listen up—this is your 60-second crash course for Work, Energy & Power in NEET.

1. Work = F·s·cosθ – Angle matters! If force and displacement are perpendicular, work = 0.
2. Work-Energy Theorem: Net work = change in kinetic energy. Use this when forces are involved.
3. Conservative forces (gravity, spring) conserve mechanical energy (KE + PE = constant).
4. Non-conservative forces (friction, applied force) change total energy. Use W_non-conservative = ΔKE + ΔPE.
5. Power = Work / Time or F·v. If speed is constant, P = F·v. Efficiency is always less than 100%.
6. NEET loves tricks: Check for friction, angles, and whether speed is constant. Convert all units to SI.

You’ve got this. Now go crush those 8-10 marks!