--- title: "Elastic and Inelastic Collisions" description: "The colliding system's momentum is conserved when net external impulse is zero, and approximately conserved when it is negligible. An elastic collision also conserves total kinetic energy. Compare the" canonical: https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq source: https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq.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`. # Elastic and Inelastic Collisions The colliding system's momentum is conserved when net external impulse is zero, and approximately conserved when it is negligible. An elastic collision also conserves total kinetic energy. Compare the kinetic-energy totals before and after to classify the collision. Subject: Science · Area: Forces & Motion · Ages 17 to 18 Page: https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq ## Ready when they can - Applies conservation of momentum in one dimension with signs that carry the directions - Totals the kinetic energy before and after and classifies the collision from the comparison - Explains how a decrease in kinetic energy can transfer energy to internal energy or sound without destroying total energy ## Lesson: Checking momentum and energy in collisions As in your momentum work, use p = m × v and signed velocities. Choose both colliding trolleys as the system. Its total momentum is conserved if net external impulse is zero, and approximately conserved if it is negligible. External impulse is the combined effect of outside forces over the collision time. Equal and opposite contact forces cancel in the system total. Use kg and m/s for momentum in kg m/s. **Example.** Right is positive. A 2 kg trolley at +4 m/s meets a 1 kg trolley at -2 m/s. Total momentum is +8 - 2 = +6 kg m/s. Net external impulse is zero. After impact, the 2 kg trolley moves at +1 m/s and carries +2 kg m/s. The other trolley must carry +6 - 2 = +4 kg m/s. Divide by its 1 kg mass: its final velocity is +4 m/s. Find each trolley's kinetic energy with KE = 0.5 × m × v², using kg and m/s to get joules. Squaring a negative velocity gives positive KE. Add both energies before impact and again after, in the same reference frame. Equal totals define an elastic collision; unequal totals mean inelastic. These questions ignore rotation and treat the stated values as exact. *(drawing: Two 1 kg trolleys have speeds 3 and 0 m/s before impact, then 0 and 3 m/s after. Both KE totals are 4.5 J, so the collision is elastic.)* Inelastic means that total kinetic energy changes. Usually it decreases, but a spring carried by a trolley can release stored energy during impact and increase it. Objects can bounce apart in an inelastic collision. If they stick together, it is perfectly inelastic. Sticking does not require the joined pair to stop. Seeing a bounce cannot replace comparing the energy totals. **Example.** When trolleys stick, divide total signed momentum by combined mass to get their shared final velocity. With zero net external impulse, a 1 kg trolley at +4 m/s joining a resting 3 kg trolley gives v = (1 × 4 + 3 × 0) ÷ 4 = +1 m/s. KE before is 0.5 × 1 × 4² = 8 J; after, use the joined mass: 0.5 × 4 × 1² = 2 J. Subtract after from before: 8 - 2 = 6 J transferred out of motion. A kinetic-energy decrease is not destruction of total energy. It can increase internal energy through heating or deformation, or transfer energy away as sound. These are possible destinations, not a required list for every collision. A permanent dent is not needed. To find the decrease, subtract total KE after from total KE before. **Recap.** Check the external impulse before conserving momentum. Compare total kinetic energy separately: unchanged means elastic; changed means inelastic. *Lesson, questions and flashcards written for this dataset. Physics references: OpenStax College Physics, chapter 8, and University Physics Volume 1, section 9.4.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Momentum and Its Conservation](https://lightmysky.com/learn/science/momentum-and-its-conservation-mt_Nn5_DMbK1_) - [Kinetic and gravitational potential stores](https://lightmysky.com/learn/science/kinetic-and-gravitational-potential-stores-mt_uD3jklaZCw) ## Optional connections - [Power as Force Times Velocity, and Efficiency](https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6) ## Opens up - [Kinetic Theory: Pressure from Molecular Motion](https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu) - [The Compton Effect and Photon Momentum](https://lightmysky.com/learn/science/the-compton-effect-and-photon-momentum-mt_wt7kdaof_P)