Theme A — Space, Time and Motion
A.3.5 Gravitational Potential Energy — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 36 of 63 1 quiz
Curriculum Equation Key Circular Motion & Gravitation LawsFast Exam Solution
a_c = v² / r | F_c = (m × v²) / r | F_g = G × (m₁ × m₂) / r² | v_orbit = √(G×M / r)
Lesson summary
A.3.5 Gravitational Potential Energy — IB PHYSICS SL notes: Calculate changes in gravitational potential energy near the Earth's surface and relate them to work done against gravity.Gravitational potential energy = the energy stored in a mass because of its position in a gravitat…
- What the symbols mean
- Weight and work
- Zero level
- Conservative force
- Ep against height
- Free fall from rest
Part 1 of 8Definition
Definition
Gravitational potential energy
Gravitational potential energy the energy stored in a mass because of its position in a gravitational field.
Raising
- Raising lifting a mass does work against the gravitational force and stores that energy.
Falling
- Falling a falling mass loses gravitational potential energy, which becomes kinetic energy.
Part 2 of 8Near-surface equation
Equation
- ΔEp = mgΔh.What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)
- ΔEp is the change in gravitational potential energy in J.
- m is the mass in kg.
- g is the gravitational field strength, 9.8 N kg−1.
- Δh is the change in height in m.
Validity
- Validity it applies only in a uniform field, such as near the Earth's surface.
Weight and work
- Weight and work mg is the weight, and weight times the vertical distance is the work done lifting at steady speed.
Zero level
- Zero level ground level is usually zero, but any position can be taken as zero for a change.
- The same reference must be used throughout a problem.
Part 3 of 8Path independence
Conservative force
- Conservative force the work done against gravity depends only on the start and end heights.
Ramp
- Ramp raising a trolley 1 m up a 5 m smooth ramp needs the same energy as lifting it 1 m vertically.
- The ramp makes the force smaller but the distance longer, with the same product mgΔh.
Part 4 of 8Graphs
Ep against height
- Ep against height a straight line through the origin with gradient mg, so the relationship is linear.
Free fall from rest
- Free fall from rest the gravitational potential energy falls linearly with distance and the kinetic energy rises linearly.
- The two lines are mirror images and their sum is constant if drag is negligible.
Against time
- Against time both graphs are parabolas, because h changes with t2.
Part 5 of 8Beyond the surface
Large distances
- Large distances mgΔh fails when g changes significantly with height.
General expression
- Ep = −GMm/r, with zero at infinity.
Negative values
- Negative values work must be done to remove the object from the field.
Agreement
- Agreement for small heights the change in −GMm/r between r and r + Δh approximates mgΔh.
Part 6 of 8Applications
1Pumped storage
- Pumped storage water is pumped uphill when electricity is cheap and released through turbines at peak demand.
2Roller coaster
- Roller coaster the first hill is the highest because its energy must supply all later kinetic energy and the friction losses.
3Skydivers at terminal speed
- Skydivers at terminal speed the lost potential energy becomes thermal energy in the air.
4Liquid
- Liquid raising volume V of density ρ through h needs ρVgh, with h measured to the centre of mass of the water.
Part 7 of 8Tips for problems
Reference level
- Reference level measure heights from the lowest point so that all values are positive.
Curved path
- Curved path use only the vertical difference between the start and the end.
Thrown ball at an angle
- Thrown ball at an angle at the top it still has horizontal kinetic energy.
- Only the vertical part of the initial kinetic energy converts to potential energy.
Estimate
- Estimate lifting 1 kg through 1 m needs about 10 J, so a 70 kg person climbing 3 m gains about 2 kJ.
Part 8 of 8More from the specification
1
Gravitational work by a hoist motor
- Gravitational work by a hoist motor winding cable around an electric motor drum does work against gravity, providing a means of height elevation.
2
Gravitational Potential Energy
- The gravitational potential energy stored in an elevated mass in a uniform gravitational field is given by Delta Ep = m * g * Delta h, representing work done against gravity.
3
Elastic Potential Energy in a Spring
- Work done in deforming an ideal spring obeying Hooke's law is stored as elastic potential energy, calculated using Ep = 1/2 * k * x2,
- where k is the spring constant and x is extension.
4
Energy Conservation and Transfer Pathways
- In any closed mechanical system, mechanical energy transfers continuously between kinetic and potential stores,
- while some energy is inevitably wasted as thermal dissipation due to friction.
5
Power Output and Efficiency
- Power represents the rate at which energy is transferred; mechanical efficiency is defined as Efficiency = (useful power output / total power input) * 100%.
- (P = Delta E / Delta t)
6
Elastic potential energy
- Elastic potential energy mechanical energy stored in a compressed or stretched spring calculated as 1/2 k x2.
7
System energy efficiency
- System energy efficiency ratio of useful power output to total power input in an energy transfer system.
8
Wasted power transfers
- Wasted power transfers frictional resistance transfers input mechanical power into non-useful thermal stores within surroundings.
9
Resultant force
- Another name for net force.
10
Final speed
- Speed at the end, v
11
Elastic
- Returns to original shape when force is removed.
12
Efficiency
- Useful output divided by total input.
13
Component
- Part of a vector along one axis.
14
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)
15
Wasted energy
- Energy transferred to stores that are not useful, usually thermal in the surroundings.
16
Mechanical energy
- Sum of kinetic and potential energy.
17
Energy transfer
- Movement of energy from one store to another.
18
Sankey diagram
- Diagram where arrow width shows energy amount.
19
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)
20
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)
Key terms
| Term | Meaning |
|---|---|
| Gravitational potential energy | The energy stored in a mass because of its position in a gravitational field |
| Gravitational field strength (g) | Force per unit mass, 9.8 N kg−1 near the Earth's surface |
| Conservative force | Force for which the work done depends only on the start and end positions |
| Uniform field | Field with the same strength and direction at all points |
| Reference level | Position chosen as zero of potential energy |
| Pumped storage | Storing energy by pumping water to a higher reservoir |
Avoid these mistakes
1
Using mgh for large height changes — g changes, so use −GMm/r.
2
Mixing different zero levels in one problem — use one reference.
3
Using the path length instead of the vertical height — use only Δh.
4
Using total initial kinetic energy to find the maximum height of an angled projectile — only the vertical part converts.
5
Taking h as the depth of a reservoir — use the height of the centre of mass above the turbine.
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