Force, Work, and Energy Mechanics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your UNDANA PMB Saintek attempt.

Topic 6 of the UNDANA PMB Saintek section bundles the high-school physics of force, work-energy, waves, electric-magnetic phenomena, plus the cellular biology strand (membrane, organelles, transport). It carries roughly 3% weightage across the PMB question paper, which means one or two questions are almost always drawn from this cluster.

Memorise these six equations — they cover ~70% of the physics prompts you’ll meet:

F = m·a (Newton II): F in newtons, m in kg, a in m/s².
W = F·s·cosθ (work): θ is the angle between force vector F and displacement s.
Eₖ = ½·m·v² (kinetic energy).
Eₚ = m·g·h (gravitational potential energy).
P = V·I (electric power).
F = B·I·L·sinθ (Lorentz force on a current-carrying wire).

For biology, lock in the organelle functions: mitochondria → ATP synthesis via aerobic respiration; ribosomes → protein synthesis; rough ER → folding/membrane insertion of proteins; Golgi apparatus → modification and packaging.

Scoring tip: The 3% slice is small but cheap — read every prompt, since one correct answer here equals several minutes saved on harder reasoning items.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Force, Work, and Energy Mechanics

Newton’s three laws frame every mechanics prompt in Topic 6. Law I (inertia) governs stationary or uniformly moving objects: net force = 0. Law II gives F = m·a, the workhorse for inclined-plane and pulley problems. Law III identifies action-reaction pairs — examiners test this with two-block systems.

Work is energy transferred via a force along a displacement. Because force and displacement are vectors, the scalar work uses the projection W = F·s·cosθ. When θ = 90° (force perpendicular to motion, e.g. normal force on a sliding block), W = 0. The work-energy theorem states W_net = ΔEₖ, which lets you bypass detailed force analysis when you know the speed change.

Conservation of Mechanical Energy

On a frictionless path, Eₘ = Eₖ + Eₚ stays constant. A common UNDANA-style prompt gives a ball of mass m dropped from height h and asks for the impact speed — set m·g·h = ½·m·v² and solve v = √(2gh).

Waves

For a mechanical wave, v = λ·f, where λ is wavelength (m) and f is frequency (Hz). Period T = 1/f. Transverse waves (e.g. light, string) oscillate perpendicular to propagation; longitudinal waves (sound) oscillate parallel.

Electricity and Magnetism

Ohm’s law V = I·R and Kirchhoff’s current/voltage laws (KCL, KVL) solve DC circuits. For power, prefer P = V·I over P = I²R when voltage is given — students often forget the V in the second form when no resistance is supplied. The right-hand rule fixes the direction of the Lorentz force on a positive charge moving in a magnetic field.

Cell Biology Core

The cell is bounded by a phospholipid bilayer membrane; transport follows concentration gradients (diffusion, osmosis) or uses ATP (active transport). Inside, the nucleus stores DNA, mitochondria generate ATP, ribosomes translate mRNA into polypeptides, the endoplasmic reticulum and Golgi apparatus modify and ship proteins.

Common Trap Patterns

Trap	Why students fall for it	Correction
Confusing work units with force units	Both involve F	Work = joule (N·m); force = newton
Using F·s instead of F·s·cosθ	Skipping vector angle	Always include θ; force along motion ≠ work alone
Mixing ½mv² with momentum mv	Both involve m and v	Eₖ is scalar energy; p = mv is vector momentum
Right-hand rule on negative charges	Rule assumes positive q	Reverse direction for electrons

Exam pointer: Topic 6 problems typically arrive as a single-line numerical MCQ — keep arithmetic tight and you’ll clear this slice in under three minutes.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge Cases in Work–Energy Problems

When friction is present, W_friction = −f_k·s removes mechanical energy. The combined statement becomes W_net = ΔEₖ, where W_net includes gravity, normal, tension, and friction contributions. A block sliding down a rough incline of angle α loses Eₚ = mgh but gains only ΔEₖ = mgh − f_k·s, giving a final speed v = √(2g(h − μ·s·cosα)) — a derivation the UNDANA examiner sometimes inverts: given v, find μ.

Variable-force problems use W = ∫F·ds. For a linear spring obeying F = −k·x, the stored elastic energy is Eₚ = ½·k·x². Oscillation period T = 2π·√(m/k) follows from Newton’s second law on the spring.

Wave Phenomena to Recognise

Superposition lets two waves add algebraically at each point. Constructive interference occurs at path difference nλ; destructive at (n + ½)λ. Standing waves on a string fixed at both ends have quantised wavelengths λₙ = 2L/n, with fundamental frequency f₁ = v/(2L). Sound intensity level in decibels uses β = 10·log(I/I₀) with I₀ = 10⁻¹² W/m².

Electromagnetic Induction

Faraday’s law states the induced EMF ε = −N·(dΦ/dt), where Φ = B·A·cosθ is the magnetic flux through a loop of N turns. Lenz’s law (the minus sign) tells you the induced current opposes the change in flux — apply it before plugging numbers, or you’ll get the sign wrong on a PMB prompt.

Cell Biology — Membrane Transport in Detail

Passive transport (diffusion, facilitated diffusion, osmosis) flows down the electrochemical gradient and needs no ATP. Active transport (Na⁺/K⁺ pump, endocytosis, exocytosis) moves solutes against the gradient and consumes ATP — the mitochondria’s ATP output is therefore essential for nerve and kidney cells. Osmosis specifically refers to water movement across a selectively permeable membrane; animal cells shrink (crenate) in hypertonic solutions and burst (lyse) in hypotonic ones.

Connections Across Topic 6

The unifying thread is energy transformation: chemical energy in glucose → ATP in mitochondria → mechanical work in muscle contraction → kinetic and potential energy of motion → electrical energy in circuits → electromagnetic radiation. Recognising this chain helps you map unfamiliar prompts to a familiar equation.

Mastery trap: Memorising the Lorentz force formula without the right-hand rule earns zero marks on directional questions — direction is worth half the credit on most UNDANA magnetic-field prompts.

Practice Prompts

A 2 kg crate slides 5 m down a 30° frictionless incline. Using W = F·s·cosθ, compute the work done by gravity, then find the final speed via the work–energy theorem. (Expected: W = 49 J, v ≈ 7 m/s.)
A loop of area 0.02 m² rotates from perpendicular (θ = 0°) to parallel (θ = 90°) to a 0.5 T field in 0.1 s. Using ε = −N·(dΦ/dt) with N = 1, calculate the average induced EMF. (Expected: ε = 0.1 V.)

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Force, Work, and Energy Mechanics