Account for two-object momentum

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: Total momentum equals the two signed supplied momenta added. Formula: a+b. Variable key: a = first signed momentum (kg·m/s), b = second signed momentum (kg·m/s)
• Distinct worked inputs and result: A distinct model has +10 and -6 kg·m/s: total +4 kg·m/s.
• Assessment case 1: Supplied case 1: first signed momentum (kg·m/s)=6; second signed momentum (kg·m/s)=-2, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?
• Assessment case 2: Supplied case 2: first signed momentum (kg·m/s)=12; second signed momentum (kg·m/s)=-5, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?
• Assessment case 3: Supplied case 3: first signed momentum (kg·m/s)=8; second signed momentum (kg·m/s)=4, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?
• Assessment case 4: Supplied case 4: first signed momentum (kg·m/s)=-9; second signed momentum (kg·m/s)=3, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?
• Assessment case 5: Supplied case 5: first signed momentum (kg·m/s)=15; second signed momentum (kg·m/s)=-7, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?
• Assessment case 6: Supplied case 6: first signed momentum (kg·m/s)=-12; second signed momentum (kg·m/s)=-4, using the explicitly named quantities. Total momentum equals the two signed supplied momenta added. What result follows?

Learn the idea

For a stated isolated collision model, total momentum is the sum of object momenta. External impulses can change it. This arithmetic uses supplied momenta, not unmeasured real collisions.

Total momentum equals the two signed supplied momenta added. The formula in the supplied model is a+b. Variable key: a = first signed momentum (kg·m/s), b = second signed momentum (kg·m/s). Add signed momenta. State the isolated-system assumption for conservation.

A distinct model has +10 and -6 kg·m/s: total +4 kg·m/s. Opposite signs can partly cancel. 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 first signed momentum (kg·m/s)=7; second signed momentum (kg·m/s)=-2. Expected result: 5 kg·m/s. Explain what changes and keep this assumption: Opposite signs can partly cancel.

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