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
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
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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
| Term | Meaning |
|---|---|
| Kinetic energy | The energy an object has because of its motion, ½mv2 |
| Work–energy theorem | Net work done on a body equals its change in kinetic energy |
| Momentum | Product of mass and velocity, p = mv |
| Stopping distance | Distance needed to bring a moving body to rest |
| Scalar | Quantity with magnitude only |
| Rotational kinetic energy | Energy 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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