Physics — Algebra and Trigonometry · 40 minutes
Suggested grades 11–12 · Unit 1: Motion and Momentum · Lesson 2 of 2
Use Signs in a Momentum Account
Calculate a one-dimensional collision and test the boundary required for conservation.
Mr. S Teaches · Original starter lesson · HS-PHYS-02 · Grade range is planning guidance.Watch, notice, discuss
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Momentum | Forces & Motion | Physics | FuseSchool
By FuseSchool - Global Education
Establish mass-times-velocity and direction before constructing the signed before/after account.
Open on YouTube: Momentum | Forces & Motion | Physics | FuseSchool (opens a new tab) ↗Introduction to Momentum, Force, Newton's Second Law, Conservation of Linear Momentum, Physics
By The Organic Chemistry Tutor
Compare conservation examples and the external-force assumption; use the lesson’s signed one-dimensional collision rather than extra cases.
Open on YouTube: Introduction to Momentum, Force, Newton's Second Law, Conservation of Linear Momentum, Physics (opens a new tab) ↗What idea from the video helps you predict a combined final velocity and explain the isolated-system assumption? Identify one useful example and one limit of the video's model or explanation.
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Learning objective
Predict a combined final velocity and explain the isolated-system assumption.
Before you begin
- Use signed numbers and solve a linear equation.
Gather your materials
- Paper or notebook
- Pencil; calculator optional for numerical work; all task data supplied below
Language to know
- momentum
- Mass multiplied by velocity, including direction.
- isolated system
- A chosen system with negligible net external impulse over the interval.
- inelastic collision
- A collision in which kinetic energy of the colliding objects is not conserved.
Understand the concept
Paper collision account: A 2 kg cart moves east at 3 m/s and a 1 kg cart west at 1 m/s. They stick together. Define east positive and assume external impulse is negligible during the collision. Total momentum before is 2(3)+1(−1)=5 kg·m/s. The combined mass is 3 kg. Conserving system momentum does not mean each cart retains its momentum or that kinetic energy is unchanged. The system boundary and collision interval matter.
Teach it step by step
- Read the account and draw signed velocity arrows for both carts.
- Calculate the initial total momentum before combining masses.
- Solve 3v=5 for the combined final velocity and state its direction.
- Cite the external-impulse assumption and explain a condition under which the simple conservation equation would need another term.
Make the thinking visible
Worked example or model response
The final velocity is 5/3≈1.67 m/s east. Treating westward speed as +1 would incorrectly give 7/3. Initial kinetic energy is 9.5 J; final kinetic energy is about 4.17 J, so translational kinetic energy decreases while energy is transferred to other forms.
Guided practice
Together model two 1 kg carts, one at 4 m/s east and one initially at rest, that stick. Find the final velocity.
Independent practice
Solve for two 2 kg carts moving at +2 m/s and −1 m/s before sticking. Compare initial and final momenta and explain why total energy conservation is compatible with lower translational kinetic energy.
Quick assessment
If the final total momentum is zero, must both carts have had zero initial momentum?
Answer key & assessment criteria
Answers and teaching guidance
- Guided: Total momentum is 4 kg·m/s and combined mass 2 kg, so final velocity is 2 m/s east.
- Independent: Initial momentum is 2(2)+2(−1)=2 kg·m/s; final velocity is 0.5 m/s east. Initial and final momentum agree, while kinetic energy can become deformation, sound or thermal energy.
- Quick check: No. Equal and opposite momenta can sum to zero even when both objects are moving.
Look for: Assess the stated objective using the concrete criteria and explanations in the answer key. Invite an alternative supported solution; distinguish a model’s prediction from an established observation.
Make it work for your learner
More support
Use separate mass and signed-velocity columns before multiplying.
Extension challenge
Add a stated external impulse of −1 kg·m/s to the independent example and determine the revised final velocity.
Verified references · Selected contributions
Standards connections
Selected NGSS high school-band contribution; full performance requires additional evidence and instruction.
Subject-content standards
These records identify the part of a subject standard practiced here. Course placement is instructional guidance; the source’s category or band remains authoritative.
Contributes to NGSS performance expectation
HS-PS2-2
NGSS · High school band
Use mathematical representations of momentum conservation in an isolated system.
Read the official performance expectation ↗Selected one-dimensional algebraic representations illustrate system momentum. Real collision measurements, external impulses and more complex interactions require further investigation.
Verified 2026-11-04. Selected contribution, not full attainment.
Supporting literacy connections
These records apply to the specified reading, writing or communication task. They do not establish subject-content alignment.
Supporting Common Core literacy connection
RST.11-12.1
Common Core · Grades 11–12
Analyze technical details, distinctions and gaps using textual evidence.
Read the official standard ↗The activity explicitly analyzes the provided technical text, table or model. It contributes selected literacy practice rather than complete grade-band reading coverage or independent subject-content alignment.
Verified 2026-11-04. Selected contribution, not full attainment.