Theme A — Space, Time and Motion
A.3.7 Conservation of Mechanical Energy — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 38 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.3.7 Conservation of Mechanical Energy — IB PHYSICS SL notes: Apply conservation of mechanical energy to problems with changes in height, speed and elastic energy, and recognise when it fails.Mechanical energy = the sum of kinetic, gravitational potential and elastic potential e…
- Non-conservative force
- Conditions
- Idealisations
- Close cases
- Perpendicular forces
- Typical transfers
Section 1 of 10Mechanical energy
Mechanical energy
Mechanical energy the sum of kinetic, gravitational potential and elastic potential energy, Emech = Ek + Ep + EH.
Conserved
- Conserved it stays constant if only conservative forces such as gravity and spring forces do work.
Non-conservative force
- Non-conservative force one such as friction that dissipates energy away from the system.
- A change in mechanical energy is the work done by non-conservative forces.
Section 2 of 10When it applies
Conditions
- Conditions no friction, drag or other dissipative forces and no other agent doing work.
Idealisations
- Idealisations smooth surfaces and negligible air resistance.
Close cases
- Close cases a heavy pendulum over a few swings, a short throw and a roller coaster with good bearings.
Perpendicular forces
- Perpendicular forces the normal force on a smooth surface or the tension in a pendulum string does no work.
Typical transfers
- Typical transfers loss in gravitational potential energy = gain in kinetic energy, and loss in elastic potential energy = gain in kinetic energy.
Section 3 of 10Method
1
Choose a reference level for height.
2
Write the total mechanical energy at the start.
3
Write the total mechanical energy at the end.
4
Set them equal: ½mu2 + mgh1 = ½mv2 + mgh2.
5
Solve; the mass often cancels.
- Result
- without friction, the speed at a given height does not depend on the mass or the path.
Section 4 of 10With dissipative forces
Equation
- Equation initial mechanical energy = final mechanical energy + energy dissipated.
Energy dissipated
- Energy dissipated it equals the work done by friction, Wf = fd, where d is the distance travelled along the surface.
Total energy
- Total energy it is still conserved.
Section 5 of 10Typical systems
Typical systems
Pendulum
- Pendulum kinetic energy is greatest at the lowest point and potential energy at the extremes.
- The speed at the bottom after release from height h is v = √(2gh), independent of mass.
Roller coaster or ramp
- Roller coaster or ramp the speed depends only on the height difference when friction is ignored.
Spring and mass
- Spring and mass energy exchanges between kinetic, gravitational and elastic forms.
Vertical circle
- Vertical circle the speed varies with height and the speed at the top must still provide the centripetal force.
Free fall, skiing, skydiving
- Free fall, skiing, skydiving they involve changes between kinetic and potential energy.
Section 6 of 10Graphs and charts
Energy against position
- Energy against position the kinetic and potential curves mirror each other and their sum is a horizontal line.
Downward-sloping sum
- Downward-sloping sum it shows energy loss.
Bar charts
- Bar charts the total bar height stays the same for conservative motion and shrinks when friction acts.
Section 7 of 10Multi-stage problems
1Chain
- Chain a block sliding down a slope, crossing a rough patch and compressing a spring can use one chain.
2Equation
- Equation initial potential energy = friction loss + final elastic energy, with kinetic energy zero at both ends.
3Rough patch
- Rough patch it removes an amount equal to the friction force times its length.
4Advantage
- Advantage the method avoids Newton's laws and time.
5Loop-the-loop
- Loop-the-loop to just complete a smooth loop, v2 ≥ gr at the top, so the start height is at least 2.5r above the bottom.
6Links
- Links energy conservation is used for simple harmonic motion and orbits, and combined with momentum in collisions.
Section 8 of 10More from the specification
1
Conservative field energy invariance
- Conservative field energy invariance neglecting frictional air resistance provides a theoretical means to equate loss of potential energy to kinetic gain.
2
Conservation of Mechanical Energy Principle
- In an ideal isolated system free from dissipative resistive forces, the total mechanical energy of an object remains constant throughout its motion.
- (kinetic plus potential, Etotal = Ek + Ep)
3
Sankey Diagrams and Energy Pathways
- Energy transformations are illustrated using a Sankey diagram where input energy divides into useful work output and wasted thermal dissipation, with arrow widths drawn proportional to energy quantities.
4
Mechanical Power of Motors
- The useful power output of an electric motor lifting water or a load against gravity is given by P = W/t = Fv, expressing the rate of mechanical energy delivery in watts (W).
5
Energy Efficiency Calculations
- The efficiency of an energy transfer device is defined as the ratio of useful energy (or power) output to total input energy (or power): Efficiency = * 100%.
- (Useful Output / Total Input)
6
Efficiency
- Useful output divided by total input.
7
Density
- Mass per unit volume.
8
Component
- Part of a vector along one axis.
9
Thermal
- A convection current in the air.
10
Wasted energy
- Energy transferred to stores that are not useful, usually thermal in the surroundings.
11
Energy density
- The energy available per unit mass or area of a resource.
12
Thermal energy
- Energy of random molecular motion, increased by friction.
13
Sankey diagram
- Diagram where arrow width shows energy amount.
14
W = Fs
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
15
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Mechanical energy | Sum of kinetic, gravitational potential and elastic potential energy |
| Conservative force | Force whose work depends only on start and end positions, such as gravity |
| Non-conservative force | Force that dissipates energy from the system, such as friction |
| Reference level | Position chosen as zero of potential energy |
| Dissipated energy | Energy transferred to thermal energy of the surroundings |
| Energy bar chart | Chart of the energy stores at one position |
Section 10 of 10Exam technique
1
Applying conservation of mechanical energy when friction acts — include the energy dissipated.
2
Using height difference along the slope — use only the vertical height.
3
Thinking a perpendicular force changes mechanical energy — it does no work.
4
Forgetting elastic energy when a spring is present — include EH.
5
Saying energy is lost to friction — it is transferred to thermal energy.
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