Calculate gravitational potential change

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: Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. Formula: a*10*b. Variable key: a = mass (kg), b = height increase (m)
• Distinct worked inputs and result: A distinct model lifts 3 kg by 2 m with g=10 m/s²: 3×10×2=60 J increase.
• Assessment case 1: Supplied case 1: mass (kg)=2; height increase (m)=3, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?
• Assessment case 2: Supplied case 2: mass (kg)=3; height increase (m)=4, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?
• Assessment case 3: Supplied case 3: mass (kg)=5; height increase (m)=2, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?
• Assessment case 4: Supplied case 4: mass (kg)=6; height increase (m)=3, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?
• Assessment case 5: Supplied case 5: mass (kg)=4; height increase (m)=5, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?
• Assessment case 6: Supplied case 6: mass (kg)=8; height increase (m)=2, using the explicitly named quantities. Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. What result follows?

Learn the idea

Near Earth, with a stated approximately uniform gravitational field, change in potential energy equals mass times g times height change. We use model g=10 m/s², not an exact universal constant.

Potential-energy increase equals mass in kilograms times model g of 10 meters per second squared times height increase in meters. The formula in the supplied model is a*10*b. Variable key: a = mass (kg), b = height increase (m). Use a height change from a stated reference. The supplied g=10 is an approximation.

A distinct model lifts 3 kg by 2 m with g=10 m/s²: 3×10×2=60 J increase. Potential energy depends on system and reference. 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; height increase (m)=3. Expected result: 90 J. Explain what changes and keep this assumption: Potential energy depends on system and reference.

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