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Science (Saintek) 3% exam weight

Work and the role of the angle

Part of the UNDANA Admission (Indonesia) study roadmap. Science (Saintek) topic scienc-005 of Science (Saintek).

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Work and the role of the angle

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Work, energy, and heat form a linked cluster of physics quantities tested in the UNDANA Saintek stream. The five formulas worth memorising cover almost every question you will meet.

  • Work: W = F · s · cosθ, where θ is measured between force and displacement vectors.
  • Kinetic energy: EK = ½ m v²; depends on the square of velocity.
  • Gravitational potential energy: EP = m g h, measured from a chosen reference height.
  • Heat: Q = m c ΔT, where ΔT must be in kelvin for unit consistency.
  • Power: P = W / t, expressing how quickly energy transfers.

Exam tip: Always state the reference level for EP and convert °C to K before any heat calculation.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Work and the role of the angle θ

Mechanical work is a scalar transfer of energy produced when a force acts along a displacement. The general form W = F · s · cosθ covers all three geometric cases: θ = 0° (full push, W positive), θ = 90° (force perpendicular to motion, W = 0, as in circular motion where centripetal force does no work), and θ = 180° (force opposing motion, W negative, such as friction slowing a sliding block).

A frequent UNDANA prompt asks for the work done by gravity on an object sliding down an incline. Here θ is the angle between the weight vector (vertical) and the displacement vector (along the slope), so cosθ equals sinα where α is the incline angle.

Kinetic and potential energy

Kinetic energy is the energy of motion. Doubling the speed of a 2 kg mass quadruples its EK, since EK ∝ v². Gravitational potential energy near Earth’s surface is computed with EP = m g h, using g ≈ 9.8 m/s² (or 10 m/s² for quick approximations).

EP is relative: only differences in EP carry physical meaning. A book at height 2 m above a table has 1 m × m × g more EP than one resting on the table, regardless of whether you measure from the floor or sea level.

Heat, temperature, and specific heat

Heat Q is energy in transit due to a temperature difference, while temperature measures average molecular kinetic energy. They are not interchangeable. Specific heat capacity c (J kg⁻¹ K⁻¹) is a material property: water ≈ 4 180, aluminium ≈ 900, copper ≈ 387.

Conservation of energy

In an isolated system, EK + EP + Q = constant. A ball dropped from height h reaches the ground with v = √(2gh) when air resistance is neglected — a direct consequence of EP converting entirely to EK.

Common exam traps

TrapCorrection
Forgetting cosθAlways include the angle between F and s
Mixing °C with KConvert ΔT to K: ΔK = Δ°C
Treating Q and T as identicalQ is energy (J); T is state (K or °C)
Ignoring sign of WNegative W when force opposes displacement
Assuming EP is absoluteEP depends on reference level chosen

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Edge cases and unit discipline

When force varies with position, the scalar product W = ∫F·ds replaces the simple F·s·cosθ. For a spring obeying Hooke’s law, F = -kx, integrating from x = 0 to x = x gives W = ½ k x², which equals the elastic potential energy stored. Students confuse this with gravitational EP because both share a ½-style coefficient; the source of the factor differs.

Power has two useful forms: P = W/t (average) and P = F·v (instantaneous, when F and v are parallel). The second form matters when a car maintains constant velocity against drag — engine power scales linearly with speed at constant force.

Heat in phase changes

The Q = m c ΔT formula applies only when no phase change occurs. To melt ice at 0 °C, use Q = m L_f where L_f (latent heat of fusion) for water is 3.34 × 10⁵ J/kg. A UNDANA question may chain both: warming ice from -10 °C to 0 °C (Q₁ = m c_ice ΔT), then melting it (Q₂ = m L_f).

Worked micro-example

A 2 kg block slides 5 m down a frictionless 30° incline. Take g = 10 m/s².

  • Height lost: h = 5 sin30° = 2.5 m.
  • EP lost: ΔEP = m g h = 2 × 10 × 2.5 = 50 J.
  • EK gained at bottom: EK = 50 J.
  • Final speed: v = √(2 EK / m) = √(50) ≈ 7.07 m/s.

This single problem tests formula selection, trigonometry, reference choice, and conservation reasoning — the exact combination UNDANA examiners favour.

Mastery here feeds directly into momentum and impulse (work-energy theorem: W_net = ΔEK), thermodynamics (first law ΔU = Q - W), and fluid mechanics (pressure-volume work).

Practice prompts

  1. A 1 500 kg car brakes from 20 m/s to rest over 50 m. Find the average braking force and the heat dissipated in the brakes.
  2. 0.5 kg of water at 20 °C receives 8 360 J of heat. Using c = 4 180 J/(kg·K), compute the final temperature.

Scoring strategy

Allocate ≤90 seconds per numeric item in UNDANA Saintek. Read for the target quantity, write down the matching formula, plug in SI units, and check for cosθ or ΔT-in-K before submitting.

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