--- title: "Kinetic and gravitational potential stores" description: "Calculate kinetic energy from mass and speed, and gravitational potential energy from mass, gravitational field strength and height. Use ideal drops and straight-up launches to find speeds and rise he" canonical: https://lightmysky.com/learn/science/kinetic-and-gravitational-potential-stores-mt_uD3jklaZCw source: https://lightmysky.com/learn/science/kinetic-and-gravitational-potential-stores-mt_uD3jklaZCw.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Kinetic and gravitational potential stores Calculate kinetic energy from mass and speed, and gravitational potential energy from mass, gravitational field strength and height. Use ideal drops and straight-up launches to find speeds and rise heights, with negligible resistance. Subject: Science · Area: Energy · Ages 15 to 16 Page: https://lightmysky.com/learn/science/kinetic-and-gravitational-potential-stores-mt_uD3jklaZCw ## Ready when they can - Calculates the kinetic store of a moving object and the gravitational store of a raised one - Equates the two stores to find a landing speed or a rise height - Explains why doubling speed makes kinetic energy four times larger when mass stays the same ## Lesson: Swapping height for speed Kinetic energy KE = 0.5 × m × v². Use mass m in kilograms and speed v in metres per second to get joules. Square the speed before multiplying. At fixed mass, doubling speed multiplies KE by four. A same-car comparison at 60 mph and 30 mph uses a ratio; do not insert mph directly into this SI equation. Near Earth's surface, gravitational potential energy GPE = mgh relative to a chosen zero height. Use mass in kilograms, height in metres and g in N/kg. Here choose the approximation g = 10 N/kg. A 0.4 kg object 5 m above the zero level has GPE = 0.4 × 10 × 5 = 20 J. **Example.** Drop that object from rest through 5 m, ignoring air resistance. Its 20 J loss of GPE equals its gain in KE. Thus 0.5 × 0.4 × v² = 20, so v² = 100 and v = 10 m/s just before impact. The energy balance uses the height lost, not the total length of a path. **Example.** For a straight-up launch, ignore air resistance and choose launch height as zero. At the highest point speed is zero, so launch KE equals gained GPE: 0.5mv² = mgh. Divide both sides by the same nonzero mass m: 0.5v² = gh. Then divide by g to get h = v² ÷ (2g). At 4 m/s with g = 10 N/kg, h = 16 ÷ 20 = 0.8 m. Multiply both sides of KE = 0.5mv² by 2, then divide by mass: v² = 2KE ÷ m. Take the positive square root to undo squaring. For a 4 kg object with 50 J of KE, v² = 100 ÷ 4 = 25. Since 5 × 5 = 25, v = 5 m/s. Speed is nonnegative; do not stop at the squared-speed value. *(drawing: For the same 1 kg object, doubling speed from 2 to 4 m/s increases calculated KE from 2 to 8 J.)* Hold mass fixed when comparing speeds. A doubled speed gives 2² = 4 times the KE. At fixed speed, doubling mass only doubles KE. A comparison must say what stays unchanged. Ideal store swaps also require negligible resistance and no other energy transfers. **Recap.** Half m v squared for motion, m g h for height, and falls swap one for the other. *Adapted from OpenStax College Physics explanations of kinetic energy, gravitational potential energy and conservation, openstax.org.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Energy stores and transfers](https://lightmysky.com/learn/science/energy-stores-and-transfers-mt_Jvg_r4yWaY) - [Calculating work done and power](https://lightmysky.com/learn/science/calculating-work-done-and-power-mt_udulQxseg1) ## Opens up - [Energy in Simple Harmonic Motion, Damping and Resonance](https://lightmysky.com/learn/science/energy-in-simple-harmonic-motion-damping-and-resonance-mt_3sh7E7k7j2) - [Elastic and Inelastic Collisions](https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq) - [Internal Energy, Absolute Zero and the Kelvin Scale](https://lightmysky.com/learn/science/internal-energy-absolute-zero-and-the-kelvin-scale-mt_n4Ku8ZDy1U) - [Stopping Distances and Braking Energy](https://lightmysky.com/learn/science/stopping-distances-and-braking-energy-mt_nRNZS4jHoj)