Use a net-force model

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: Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. Formula: a*b. Variable key: a = mass (kg), b = signed acceleration (m/s²)
• Distinct worked inputs and result: A distinct model has 3 kg mass and -2 m/s² acceleration: 3×(-2)=-6 N.
• Assessment case 1: Supplied case 1: mass (kg)=2; signed acceleration (m/s²)=3, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?
• Assessment case 2: Supplied case 2: mass (kg)=4; signed acceleration (m/s²)=-2, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?
• Assessment case 3: Supplied case 3: mass (kg)=5; signed acceleration (m/s²)=4, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?
• Assessment case 4: Supplied case 4: mass (kg)=6; signed acceleration (m/s²)=-3, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?
• Assessment case 5: Supplied case 5: mass (kg)=8; signed acceleration (m/s²)=2, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?
• Assessment case 6: Supplied case 6: mass (kg)=10; signed acceleration (m/s²)=0.5, using the explicitly named quantities. Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. What result follows?

Learn the idea

Newton’s second law relates net force to mass times acceleration in this nonrelativistic inertial-frame model. Individual forces must first be combined; the equation uses net force.

Net force equals mass in kilograms multiplied by signed acceleration in meters per second squared. The formula in the supplied model is a*b. Variable key: a = mass (kg), b = signed acceleration (m/s²). Use net force rather than a single force when others act. A newton is kg·m/s².

A distinct model has 3 kg mass and -2 m/s² acceleration: 3×(-2)=-6 N. Keep acceleration’s sign. 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 mass (kg)=3; signed acceleration (m/s²)=3. Expected result: 9 N. Explain what changes and keep this assumption: Keep acceleration’s sign.

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