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Theme A — Space, Time and Motion

A.3.4 Kinetic Energy — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 35 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
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Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.3.4 Kinetic Energy — IB PHYSICS SL notes: Use the expression for kinetic energy and the work–energy theorem to relate speed, mass and energy changes.Kinetic energy Ek = the energy an object has because it is moving.Equation — Ek = ½mv2.What the symbols mean: Ek = kinetic energy…

  • Squared speed
  • Falling object
  • Maintained
  • Momentum form
  • Collisions
  • Derivation

Part 1 of 7Definition

Kinetic energy Ek
Kinetic energy Ek the energy an object has because it is moving.
Equation
  • Ek = ½mv2.
    What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
  • Ek is in J, m in kg and v in m s−1.
Scalar
  • Scalar it is never negative, so a loss of kinetic energy is stated without a minus sign.
Squared speed
  • Squared speed only v is squared, not m.
  • Doubling the speed quadruples the kinetic energy and doubling the mass only doubles it.
Falling object
  • Falling object it gains kinetic energy as it loses gravitational potential energy.
Maintained
  • Maintained a body keeps its kinetic energy unless its speed or mass changes.

Part 2 of 7In terms of momentum

Momentum form
  • Ek = p2/2m, where p is the momentum in kg m s−1.
Check
  • (mv)2/2m = m2v2/2m = ½mv2.
Use
  • Use it is helpful in particle physics and collisions, to compare bodies with the same momentum.
Collisions
  • Collisions momentum is conserved in all collisions without external force, but kinetic energy only in elastic ones.

Part 3 of 7Work–energy theorem

Derivation
  • Derivation a constant net force F over displacement s gives W = Fs = mas.
  • With v2 = u2 + 2as this becomes W = ½mv2 − ½mu2.
Theorem
  • Theorem the net work done on an object equals its change in kinetic energy, Wnet = ΔEk.
All forces
  • All forces include every force, with its sign.
Advantage
  • Advantage speeds and stopping distances are found without using time.

Part 4 of 7Stopping distance

Braking
  • Braking a braking force F over a distance d removes the kinetic energy, Fd = ½mv2, so d = mv2/(2F).
Proportion
  • Proportion the distance is proportional to v2, so doubling the speed means four times the distance.
Crumple zones
  • Crumple zones they lengthen the stopping distance, so the average force F = ΔEk/d is smaller.
Speed limits
  • Speed limits a modest rise in speed gives a disproportionate rise in the energy to be absorbed in a crash.

Part 5 of 7Graphs

1Ek against v
  • Ek against v a parabola through the origin.
2Ek against v2
  • Ek against v2 a straight line through the origin with gradient ½m.
3Ek against time in free fall from rest
  • Ek against time in free fall from rest a parabola, since v is proportional to t.
4Net force–displacement graph
  • Net force–displacement graph the area equals the change in kinetic energy.

Part 6 of 7Practical points

Units
  • Units convert km h−1 to m s−1 by dividing by 3.6; 90 km h−1 is 25 m s−1.
Extreme cases
  • Extreme cases zero speed gives zero energy and a tenth of the speed gives a hundredth of the energy.
Changing mass
  • Changing mass recalculate Ek with the current mass, as for a rocket burning fuel.
Frame of reference
  • Frame of reference a train passenger has no kinetic energy relative to the train but a large one relative to the ground.
Rotation
  • Rotation a spinning body also has rotational kinetic energy ½Iω2, so a rolling wheel has more than ½mv2.

Part 7 of 7More from the specification

More from the specification
Rotational kinetic energy of an electric motor
  • Rotational kinetic energy of an electric motor supplying electrical energy accelerates spinning motor armatures, accumulating rotational kinetic energy.
Kinetic energy formula and derivation
  • Translational kinetic energy is given by Ek = 0.5 * m * v2, representing the mechanical work required to accelerate mass m from rest to speed v.
Elastic potential energy in springs
  • Work done stretching an ideal spring obeying Hooke's law (F = kx) is stored as elastic potential energy: Ep = 0.5 * k * x2.
    What the symbols mean: F = force (N) · k = spring constant (N m−1) · x or e = extension (m)
Energy efficiency and dissipation
  • Energy efficiency is the ratio of useful energy output to total energy input;
    • non-conservative resistive forces dissipate mechanical energy into thermal energy.
Mechanical work-energy theorem
  • Mechanical work-energy theorem net mechanical work done on a body equals total change in its kinetic energy store.
Elastic spring energy
  • Elastic spring energy compressing a horizontal spring stores elastic potential energy that transfers completely into kinetic energy when released.
Power efficiency of systems
  • Power efficiency of systems ratio of useful kinetic power output to total supplied mechanical power, with remainder wasted as heat.
Mechanical energy
  • Sum of kinetic and potential energy.
Sankey diagram
  • Diagram where arrow width shows energy amount.
Energy conservation
  • Mgh = ½Mv2 + ½Iω2.
Resultant force
  • Another name for net force.
Final speed
  • Speed at the end, v
Efficiency
  • Useful output divided by total input.
Friction
  • Force parallel to the surface opposing relative motion or its tendency.
Density
  • Mass per unit volume.
Component
  • Part of a vector along one axis.
Thermal
  • A convection current in the air.
Position
  • Location relative to a reference point.
Energy transferred
  • W = V Q, in joules.
    What the symbols mean: E or W = energy transferred (J) · Q = charge (C) · V = potential difference (V) · I = current (A) · t = time (s)
Wasted energy
  • Energy transferred to stores that are not useful, usually thermal in the surroundings.

Key terms

TermMeaning
Kinetic energyThe energy an object has because of its motion, ½mv2
Work–energy theoremNet work done on a body equals its change in kinetic energy
MomentumProduct of mass and velocity, p = mv
Stopping distanceDistance needed to bring a moving body to rest
ScalarQuantity with magnitude only
Rotational kinetic energyEnergy of a spinning body, ½Iω2

Avoid these mistakes

1
Squaring the mass or forgetting to square the speed — only v is squared.
2
Giving a loss of kinetic energy a negative sign — energy is a scalar.
3
Using km h−1 directly in the formula — convert to m s−1.
4
Assuming kinetic energy is conserved in all collisions — only in elastic ones.
5
Saying doubling the speed doubles the energy — it quadruples it.

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