KINETIC ENERGY (Ek) is the energy stored in any moving object.
EQUATION:
Ek = ½ × m × v²
Ek = kinetic energy (J)
m = mass (kg)
v = speed (m/s)
Key points:
Kinetic energy depends on the SQUARE of speed — doubling speed QUADRUPLES kinetic energy.
Any moving object has kinetic energy: cars, wind, flowing water, planets.
EXAMPLE:
1000 kg car at 20 m/s:
Ek = ½ × 1000 × 20² = ½ × 1000 × 400 = 200,000 J = 200 kJ
Gravitational Potential Energy
GRAVITATIONAL POTENTIAL ENERGY (Ep) is the energy stored in an object due to its HEIGHT above the ground.
EQUATION:
Ep = m × g × h
Ep = gravitational potential energy (J)
m = mass (kg)
g = gravitational field strength (N/kg) — on Earth: g = 9.8 N/kg
h = height above ground (m)
Key points:
GPE increases as height increases.
GPE depends on mass — heavier objects store more GPE at the same height.
g = 9.8 N/kg on Earth; use g = 10 N/kg for estimates.
EXAMPLE:
2 kg book on a shelf 1.5 m above the floor:
Ep = 2 × 9.8 × 1.5 = 29.4 J
Elastic Potential Energy
ELASTIC POTENTIAL ENERGY (Ee) is the energy stored in a stretched or compressed elastic object.
EQUATION:
Ee = ½ × k × e²
Ee = elastic potential energy (J)
k = spring constant (N/m) — stiffness of the spring
e = extension or compression (m)
Key points:
Only valid within the ELASTIC LIMIT (Hooke's Law region).
A stiffer spring (larger k) stores more energy for the same extension.
Elastic PE depends on extension SQUARED — doubling extension quadruples stored energy.
EXAMPLE:
Spring with k = 200 N/m stretched 0.05 m:
Ee = ½ × 200 × 0.05² = ½ × 200 × 0.0025 = 0.25 J
⚠️ Common Mistake
In Ek = ½mv², SQUARE THE SPEED FIRST before multiplying. Write out v² before doing anything else. Also: mass in kg, speed in m/s. Convert 500 g → 0.5 kg and 72 km/h → 20 m/s before substituting.
📐 Variables
EkKinetic energy (Ek) is measured in joules (J)
EpGravitational potential energy (Ep) is measured in joules (J)
EeElastic potential energy (Ee) is measured in joules (J)
mMass (m) is measured in kilograms (kg)
vSpeed (v) is measured in m/s (m/s)
gGravitational field strength (g) is measured in N/kg (N/kg)
hHeight (h) is measured in metres (m)
kSpring constant (k) is measured in N/m (N/m)
eExtension (e) is measured in metres (m)
📐 Key Equations
Ek = ½ × m × v²
Ep = m × g × h
Ee = ½ × k × e²
📌 Key Note
Ek = ½mv² (kinetic). Ep = mgh (gravitational PE, g = 9.8 N/kg Earth). Ee = ½ke² (elastic PE). Doubling speed → ×4 kinetic energy. Doubling extension → ×4 elastic PE. All three equations need mass in kg and distance in m.
🎯 Matching Activity — Energy Equation Match
Match each energy type to its equation. — drag the symbols on the right to match the component names on the left.
Kinetic energy
Drop here
Gravitational PE
Drop here
Elastic PE
Drop here
g on Earth
Drop here
9.8 N/kg — or 10 N/kg used for estimates
Ee = ½ke² — depends on spring constant and extension squared
Ek = ½mv² — depends on mass and speed squared
Ep = mgh — depends on mass, gravitational field strength, and height
⚽ FIFA Worked Examples
Kinetic Energy
A 70 kg cyclist travels at 6 m/s. Calculate the kinetic energy.
F
Ek = ½ × m × v²
I
m = 70 kg, v = 6 m/s
F
v² = 6² = 36; Ek = ½ × 70 × 36 = ½ × 2520
A
Ek = 1260 J
Gravitational PE
A 5 kg box is lifted 3 m. Calculate the GPE gained. (g = 9.8 N/kg)
F
Ep = m × g × h
I
m = 5 kg, g = 9.8 N/kg, h = 3 m
F
Ep = 5 × 9.8 × 3 = 5 × 29.4
A
Ep = 147 J
🎯 Test Yourself
Question 1 of 2
1. An 800 kg car travels at 20 m/s. What is its kinetic energy?
2. A spring with k = 400 N/m is compressed 0.1 m. What elastic PE is stored?
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