MCAT Physics · Lesson 2

Work and Energy

3 min read3 sectionsUpdated January 3, 2026

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2.1Energy
2.2Work
2.3Mechanical Advantage

3 sections

2.1 Energy

This section defines energy, its different forms, and how it is conserved or transferred. Covers kinetic, potential, and mechanical energy, as well as conservative vs nonconservative forces.

Energy
- System's ability to do work → make something happen
Kinetic Energy
- Formula: $KE = \frac{1}{2} m v^2$
- Energy of motion, SI unit: Joule (kg·m²/s²)
- Example: Sliding down ramp → use velocity & mass in equation
Potential Energy
- Associated with position
- Gravitational PE: $U = mgh$ (datum = zero energy position)
- Elastic PE: $U = \frac{1}{2} k x^2$ (k = spring constant, x = displacement)
Total Mechanical Energy
- $E = U + K$
- First law of thermodynamics → energy conserved, losses appear as heat in open system
- Conservative forces: gravity, electrostatic → round trip path change = 0
- Convection is heat transfer, not force
- $\Delta E = \Delta U + \Delta K = 0$ (also equals work by nonconservative forces)
- Example: Throwing baseball → work done by air resistance = energy lost
  - $\frac{1}{2} m (V_f^2 - V_i^2)$

2.2 Work

Defines work as energy transfer, describes calculations for different forces, and introduces power and the work-energy theorem.

Work
- Process transferring energy between systems (not a form of energy itself)
- SI unit: Joule
- Only two energy transfer methods: work & heat
- Stationary object → no work done
- Formula: $W = F d \cos \Theta$ $W = F d cos Θ$
  - F = magnitude of applied force
  - d = displacement magnitude
  - Θ = angle between force & displacement (dot product)
- Example: Uniform circular motion → force ⊥ displacement → W = 0
Pressure and Volume
- Pressure & volume inversely related
- Work = area under P-V curve
- Gas expansion → +W, compression → -W
- Isochoric (constant volume) → W = 0
- Isobaric (constant pressure) → $W = P \Delta V$
- Variable pressure → $W = \Delta P \Delta V$
Power
- Rate of energy transfer: $P = W/t = \Delta E/t$
- SI unit: Watt (J/s)
- Measures rate of energy expenditure over time
- Example: 300 hp car → given unlimited time, could reach unlimited velocity
Work-Energy Theorem
- Relation between work & kinetic energy: $W_\text{net} = \Delta K = K_f - K_i$
- Allows calculation of work without knowing individual forces/displacements
- Work done ∝ change in KE of object

2.3 Mechanical Advantage

Explains how simple machines reduce required force, distribute work over distance, and define mechanical efficiency.

Simple Machines
- Inclined plane
- Wedge (2 inclined planes)
- Wheel & axle
- Pulley
- Screw (rotating inclined plane)
Mechanical Advantage (MA)
- Ratio: $\text{MA} = F_\text{out}/F_\text{in}$
- Compares force exerted by machine to force applied
Inclined Plane
- Force required: $F = mg \sin \theta$
- Work done: cos θ → always = 1
Pulleys
- Reduce necessary force at cost of increased distance
- Single rope → force = mg
- Multiple ropes → force distributed (T₁ + T₂ = mg)
  - Each rope supports half the weight → half force required
  - Must pull rope twice as far to lift object same height
- Accelerating box: $2T - mg = ma$
Efficiency
- No machine 100% efficient
- $\text{Efficiency} = \frac{W_\text{out}}{W_\text{in}} = \frac{(\text{load})(\text{load distance})}{(\text{effort})(\text{effort distance})}$
- Expressed as percentage
- Compares output vs input work

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