--- title: "Unit 4.3 | Collisions and Explosions" description: "Solve elastic and inelastic collisions for AP Physics 1: objects that stick, objects that bounce, explosions and recoil, and lost kinetic energy." featured_image: "https://nerd-notes.com/wp-content/uploads/2026/10/billiard-balls-colliding-elastic-inelastic-collisions.jpg" url: "https://nerd-notes.com/unit-4-3-collisions-and-explosions/" date_modified: "2026-10-31T09:35:18+00:00" --- # Unit 4.3 | Collisions and Explosions ## Attribution Guidelines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarizing, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-4-3-collisions-and-explosions/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-4-3-collisions-and-explosions/ Momentum is conserved in every collision, kinetic energy only sometimes. This lesson covers the three setups you will see: stick, bounce and explode. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Unit 4 Breakdown You are on Lesson 3 of 4 1. [Unit 4.1 | Momentum and Impulse](https://nerd-notes.com/unit-4-1-momentum-and-impulse/) 2. [Unit 4.2 | Conservation of Momentum](https://nerd-notes.com/unit-4-2-conservation-of-momentum/) 3. [Unit 4.3 | Collisions and Explosions](https://nerd-notes.com/unit-4-3-collisions-and-explosions/) 4. [Unit 4.4 | Momentum and Energy Together](https://nerd-notes.com/unit-4-4-momentum-and-energy-together/) #### In this lesson:  - Use the momentum framework on every collision and explosion - Tell elastic and inelastic collisions apart, and spot the perfectly inelastic ones - The 3 problem types: stick together, bounce apart, and explosions and recoil [Remove Ads](https://nerd-notes.com/pricing/?for=students) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=top) ### Introduction This lesson covers **collisions and explosions**: the momentum problems you will see most on the AP exam, and how to tell elastic and inelastic collisions apart. During a quick collision or explosion, outside forces like friction barely matter, so the total momentum is conserved ([Unit 4.2](https://nerd-notes.com/unit-4-2-conservation-of-momentum/)). Every problem here is the same momentum framework: pick the system, sketch before and after, apply [katex] \sum p_i = \sum p_f [/katex]. What changes is the setup. [Remove Ads](https://nerd-notes.com/pricing/?for=students) ### Three Kinds of Collisions *Momentum is conserved in every collision. Kinetic energy is conserved only in elastic ones.* | **Type** | **What happens** | **Equations** | | --- | --- | --- | | Elastic | Objects bounce apart; no kinetic energy lost | [katex] \sum p_i = \sum p_f [/katex] and [katex] \sum KE_i = \sum KE_f [/katex] | | Inelastic | Objects bounce, some KE becomes heat, sound, or deformation | [katex] \sum p_i = \sum p_f [/katex] only | | Perfectly inelastic | Objects stick and move together; the most KE possible is lost | [katex] m_1v_1 + m_2v_2 = (m_1 + m_2)v’ [/katex] | [Remove Ads](https://nerd-notes.com/pricing/?for=students) “Momentum is conserved but energy is lost” sounds like a contradiction. It isn’t: the *total* energy is conserved, but kinetic energy turns into thermal energy and sound, just like friction in Unit 3.3. Equal carts, one at rest: how much kinetic energy survives nerd-notes.com *When two equal carts stick together, they keep half the speed and therefore half the kinetic energy.* ### Conceptual Practice Three quick checks on what is conserved, before any math. [Open in UBQ](https://nerd-notes.com/ubq/122456/) Question 12 A block of mass m slides with a constant speed v₀ across a horizontal, frictionless surface toward a stationary block of mass 2m. The two blocks… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/122543/) Question 13 Cart 1 of mass m moves with initial speed v₀ and kinetic energy K₀ along a horizontal, frictionless track toward an identical Cart 2 that is… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/109334/) Question 14 A cart of mass M moves with speed v₀ on a horizontal frictionless track toward a second cart of mass 3M that is initially at rest. The carts collide… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) \(P_i = P_f\) – The Momentum Problem Solving Framework Official course · step-by-step video walkthrough [Watch · 21 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=video-mid#course=94339&module=94420&lesson=102946) ### Problem Type 1: Stick together **How to spot it:** “Stick”, “lock together”, “embed”, “move off as one”. **Setup:** [katex] m_1v_1 + m_2v_2 = (m_1 + m_2)v’ [/katex]. One unknown, one equation. If the question asks about energy, compare kinetic energy before and after. A [katex] 1200\,\text{kg} [/katex] car moving at [katex] 15.6\,\text{m/s} [/katex] hits a stationary [katex] 1500\,\text{kg} [/katex] car. They lock together. How fast do they move, and how much kinetic energy is lost? **Momentum:** [katex] (1200)(15.6) + 0 = (2700)v’ \rightarrow v’ \approx 6.93 \, m/s [/katex] **Energy before:** [katex] \frac{1}{2}(1200)(15.6)^2 \approx 146{,}000 \, J [/katex]. **After:** [katex] \frac{1}{2}(2700)(6.93)^2 \approx 65{,}000 \, J [/katex]. About [katex] 81{,}000\,\text{J} [/katex] (more than half) went into crumpling metal, heat and sound. [Remove Ads](https://nerd-notes.com/pricing/?for=students) **AP trap:** Using conservation of kinetic energy to find the final speed. Objects that stick always lose kinetic energy, so only momentum works. [Open in UBQ](https://nerd-notes.com/ubq/24725/) Question 15 A block with mass m slides at speed v₀ on a smooth surface and hits a stationary block with mass M. They stick together and move at speed (v₀/3)… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/39119/) Question 16 A 1.0 kg lump of clay is sliding to the right on a frictionless surface with a speed of 2 m/s. It collides head-on and sticks to a 0.5 kg metal… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/29591/) Question 17 A 1.0-kg object is moving with a velocity of 6.0 m/s to the right. It collides and sticks to a 2.0-kg object moving with a velocity of 3.0 m/s in the… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=mid) ### Problem Type 2: Bounce apart **How to spot it:** “Bounces”, “rebounds”, “elastic”, or two different final velocities. **Setup:** Momentum gives one equation with signs. To decide if the collision was elastic, compare the total kinetic energy before and after. A [katex] 2\,\text{kg} [/katex] cart at [katex] 6\,\text{m/s} [/katex] hits a [katex] 4\,\text{kg} [/katex] cart at rest. Afterward the [katex] 2\,\text{kg} [/katex] cart rolls back at [katex] 2\,\text{m/s} [/katex]. How fast does the [katex] 4\,\text{kg} [/katex] cart move? Was the collision elastic? [Remove Ads](https://nerd-notes.com/pricing/?for=students) **Momentum** (right is positive): [katex] (2)(6) + 0 = (2)(-2) + (4)v \rightarrow v = 4 \, m/s [/katex]. **Energy before:** [katex] \frac{1}{2}(2)(6)^2 = 36 \, J [/katex]. **After:** [katex] \frac{1}{2}(2)(2)^2 + \frac{1}{2}(4)(4)^2 = 4 + 32 = 36 \, J [/katex]. No kinetic energy lost, so it was elastic. **AP trap:** Dropping the minus sign on the cart that bounces back. With it, you get the right answer; without it, the [katex] 4\,\text{kg} [/katex] cart would have to move at [katex] 2\,\text{m/s} [/katex] and the energy check fails. [Open in UBQ](https://nerd-notes.com/ubq/91373/) Question 18 You are lying in bed and want to shut your bedroom door. You have a bouncy "superball" and a blob of clay, both with the same mass m. Which one would… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/22815/) Question 19 A bowling ball moving with speed v collides head-on with a stationary tennis ball. The collision is elastic and there is no friction. The bowling… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) Applying Momentum In 2D Official course · step-by-step video walkthrough [Watch · 17 min](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=video-mid2#course=94339&module=94420&lesson=103414) ### Problem Type 3: Explosions and recoil **How to spot it:** Everything starts at rest (or moving together) and flies apart: guns, skaters pushing off, a spring between two carts, a firework. **Setup:** The total momentum before is zero (or one shared value), so [katex] 0 = m_1v_1′ + m_2v_2′ [/katex]. The pieces leave with equal and opposite momentum. \(p_{\text{total}} = 0\) \(\textcolor{#0072FF}{-}p\) \(\textcolor{#0072FF}{+}p\) \(p_{\text{total}} = -p + p = 0\) *Before: total momentum is zero. After: equal and opposite momenta, so the total is still zero.* A [katex] 45\,\text{kg} [/katex] skater and a [katex] 60\,\text{kg} [/katex] skater push off each other from rest. The [katex] 45\,\text{kg} [/katex] skater moves at [katex] 0.375\,\text{m/s} [/katex]. How fast does the [katex] 60\,\text{kg} [/katex] skater move? [Remove Ads](https://nerd-notes.com/pricing/?for=students) [katex] 0 = (45)(-0.375) + (60)v \rightarrow v = 0.28 \, m/s [/katex] in the opposite direction. The heavier skater moves slower, but with the same size momentum. Guns recoil, rockets fly and swimmers push off walls for the same reason. **AP trap:** Thinking an explosion breaks conservation of momentum because kinetic energy appears from nowhere. The kinetic energy comes from chemical or spring energy; the momentum still adds to zero. [Open in UBQ](https://nerd-notes.com/ubq/22795/) Question 20 A child ( m = 32 kg) in a boat ( m = 71 kg) throws a 7.1 kg package out horizontally with a speed of 12.2 m/s. Calculate the velocity of the boat… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/91332/) Question 21 Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/122548/) Question 22 An isolated object at rest on a horizontal, frictionless surface explodes into three distinct fragments that move along the surface. In a coordinate… Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Remove Ads](https://nerd-notes.com/pricing/?for=students) Conservation of Momentum Practice Official course · graded, with step-by-step explanations [Practice](https://nerd-notes.com/courses/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=practice-practice#course=94339&module=94420&lesson=98990) Quiz Lab Collisions: Elastic and Inelastic Carts and balls that bounce, stick or crumple. Momentum is always conserved; kinetic energy only sometimes. 15 questions · Free [Take the quiz](https://nerd-notes.com/quiz/?id=173) Learn Physics from Scratch The only course that teaches you to solve problems with dead-simple frameworks that make physics look easy. - Self-paced - About 12 weeks - ★ 4.9 · 12,000+ students [Enroll here](https://nerd-notes.com/physics/ap-physics-1-from-scratch-course/?utm_source=blog&utm_medium=article&utm_campaign=unit-4-3-collisions-and-explosions&utm_content=end) ### Lesson 4.4 Preview In the [final lesson](https://nerd-notes.com/unit-4-4-momentum-and-energy-together/) of this unit we chain momentum and energy together for the hardest problems: a collision followed by a swing, a slide or a spring. ## Attribution Guidelines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarizing, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-4-3-collisions-and-explosions/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-4-3-collisions-and-explosions/