Find mechanical energy remaining

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Remaining mechanical energy equals initial mechanical energy minus thermal transfer. Formula: a-b. Variable key: a = initial mechanical energy (J), b = thermal transfer (J)
• Distinct worked inputs and result: A distinct model starts with 70 J mechanical energy and transfers 12 J thermally: 70-12=58 J remains mechanical.
• Assessment case 1: Supplied case 1: initial mechanical energy (J)=100; thermal transfer (J)=20, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?
• Assessment case 2: Supplied case 2: initial mechanical energy (J)=150; thermal transfer (J)=35, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?
• Assessment case 3: Supplied case 3: initial mechanical energy (J)=200; thermal transfer (J)=50, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?
• Assessment case 4: Supplied case 4: initial mechanical energy (J)=80; thermal transfer (J)=15, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?
• Assessment case 5: Supplied case 5: initial mechanical energy (J)=240; thermal transfer (J)=60, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?
• Assessment case 6: Supplied case 6: initial mechanical energy (J)=300; thermal transfer (J)=90, using the explicitly named quantities. Remaining mechanical energy equals initial mechanical energy minus thermal transfer. What result follows?

Learn the idea

If some mechanical energy transfers into thermal processes, total energy remains conserved while mechanical energy decreases. The model supplies all transfers and excludes extra work input.

Remaining mechanical energy equals initial mechanical energy minus thermal transfer. The formula in the supplied model is a-b. Variable key: a = initial mechanical energy (J), b = thermal transfer (J). Do not say transferred energy is destroyed. Mechanical energy and total energy differ.

A distinct model starts with 70 J mechanical energy and transfers 12 J thermally: 70-12=58 J remains mechanical. Use the supplied complete accounting boundary. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with initial mechanical energy (J)=101; thermal transfer (J)=20. Expected result: 81 J. Explain what changes and keep this assumption: Use the supplied complete accounting boundary.

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