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Physics — Algebra and Trigonometry · 35 minutes

Suggested grades 11–12 · Unit 2: Energy and Waves · Lesson 1 of 2

Account for Energy With a Repeatable Algorithm

Construct a paper calculation model that includes transfers outside the chosen mechanical-energy account.

Mr. S Teaches · Original starter lesson · HS-PHYS-03 · Grade range is planning guidance.

Watch, notice, discuss

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After watching

What idea from the video helps you calculate an energy budget and write a repeatable sequence for predicting kinetic energy and speed? Identify one useful example and one limit of the video's model or explanation.

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Learning objective

Calculate an energy budget and write a repeatable sequence for predicting kinetic energy and speed.

Before you begin

  • Use squares, square roots and gravitational energy mgh.

Gather your materials

  • Paper or notebook
  • Pencil; calculator optional for numerical work; all task data supplied below

Language to know

system boundary
A choice defining what is included in an energy account.
kinetic energy
Energy associated with motion, modeled here as mv²/2.
algorithm
An explicit sequence of steps producing an output from inputs.

Understand the concept

Model account: A 2 kg object begins at rest 10 m above a reference level. Use g=10 m/s². Initial gravitational energy is 200 J. A supplied pathway transfers 50 J from the selected mechanical account to thermal energy in the object and surroundings before the bottom. Predict final kinetic energy by subtracting that transfer, then solve K=mv²/2. The model assumes no other initial energy or transfer; a paper algorithm is a precursor to, not a completed computer simulation.

Teach it step by step

  1. Read the account and list inputs m, g, h and thermal transfer with units.
  2. Write the sequence: calculate mgh, subtract the specified transfer, check that K is nonnegative, then compute speed.
  3. Apply the sequence and draw an energy bar account totaling the initial 200 J.
  4. Explain a gap or inconsistent input, such as transfer greater than available initial energy, rather than taking a square root of a negative K.

Make the thinking visible

Worked example or model response

K=200−50=150 J. Since K=(2v²)/2=v², v=√150≈12.25 m/s. A 200 J initial bar becomes 150 J kinetic plus 50 J transferred from the chosen mechanical account, not 50 J of destroyed energy.

Guided practice

Together run the algorithm for the same object and height with 80 J transferred from the mechanical account.

Independent practice

Write pseudocode or a numbered calculation rule and apply it for h=5 m with 20 J transferred. Identify which measurement would be needed to compare the prediction with a real path.

Quick assessment

Would an algorithm using only height predict the same speed on every real path?

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: K=120 J and speed √120≈10.95 m/s.
  2. Independent: Initial energy is 100 J; K=80 J; speed √80≈8.94 m/s. A useful test needs motion measurements and evidence about energy transfers or losses from the selected account.
  3. Quick check: No. Path-dependent transfers and other conditions matter; the simple prediction depends on its explicit assumptions.

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 energy bars first and supply the square-root step as a formula card.

Extension challenge

Implement the paper algorithm in a spreadsheet, vary height and transfer independently and explain invalid inputs rather than silently discarding them.

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-PS3-1

NGSS · High school band

Represent changes and transfers in a system’s energy mathematically.

Read the official performance expectation ↗

This supplies an algebraic budget and paper algorithm toward computational modeling. It does not implement or validate a computational model, and only selected energy components are represented.

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.