What is shared by two inverse-square interactions?
Submit: An evidence record, explanation and revision.
Related lesson: Electricity and Magnetism
This is a teacher-led extension beyond the short lesson. The task supplies a performance opportunity; completion alone does not certify mastery, full NGSS coverage or state alignment.
Teacher review guideBuild the idea
For two point-like objects, gravitational force magnitude is Gm₁m₂/r² and is attractive. Electric force magnitude is k|q₁q₂|/r²; opposite charges attract and like charges repel. Use center-to-center separation. These idealizations do not directly describe every extended or many-object system.
Science / engineering practice
Using mathematics and computational thinkingCore idea
Gravitational and electric forces follow quantitative relationshipsCrosscutting concept
PatternsEvidence and model inputs
Calculation cards: G=6.67×10⁻¹¹ N·m²/kg²; masses 2 kg and 3 kg separated by 0.50 m. k=8.99×10⁹ N·m²/C²; charges +2×10⁻⁶ C and −3×10⁻⁶ C separated by 0.30 m. Compare each with doubled separation, keeping the other quantities fixed.
Keep actual observations, published findings and invented model cases labeled separately. If a source or required equipment is unavailable, pause that part with a teacher; do not invent results.
Materials and preparation
Paper, graph paper or spreadsheet, and the linked readings.
Grade-level scope
Two-object algebraic models; no calculus or many-body derivations required.
Do the work
- Draw each pair with distance and direction labels.
- Calculate both original force magnitudes and report units.
- Predict the factor change for doubled separation before recalculating.
- Compare the roles of mass, charge sign and distance; explain what the common equation structure supports.
- State the point-object approximation and why a many-object case would need additional analysis.
Learner worksheet
Write on paper or type here and print. Entries stay in this page’s memory and are lost when you leave or reload; they are not saved or submitted.
Check your reasoning
- What is gravitational force magnitude?
- What is electric force magnitude and direction?
- What happens at twice the separation?
- Can gravity repel because a mass is negative in this classroom model?
Teacher review guide
Review the actual deliverable and discuss the reasoning. For each criterion, use 0 when evidence is absent or fundamentally incorrect, 1 when partly supported with a material error or omission, and 2 when accurate, supported and complete for the stated task. Maximum 8 points is a task score, not a proficiency certification. Give feedback and allow revision.
- Represents two-object interactions with correct directions.
- Uses SI quantities and computes magnitudes correctly.
- Explains inverse-square comparisons mathematically.
- Distinguishes charge sign from mass and states model limits.
Answer guidance for the reasoning checks
What is gravitational force magnitude?
6.67×10⁻¹¹×6/0.25 = 1.6008×10⁻⁹ N.
What is electric force magnitude and direction?
8.99×10⁹×6×10⁻¹²/0.09 ≈ 0.599 N, attractive.
What happens at twice the separation?
Each magnitude becomes one-fourth.
Can gravity repel because a mass is negative in this classroom model?
No. The modeled masses are positive and gravity is attractive.
Access, support and extension
Offer read-aloud support, labeled diagrams, larger print or an oral/recorded explanation while preserving the scientific reasoning. A partner or teacher can handle physical manipulation while the learner plans, records and interprets. Use a teacher-provided measured dataset only when its provenance and limitations are explicit; it does not replace conducting an investigation when that is the assessed practice. For greater independence, remove prompts and ask learners to compare a second explanation or test another justified revision.
Sources and standard reference
- Official NGSS HS-PS2-4 performance expectation — inspect the practice, core idea, crosscutting concept and assessment boundary.
Instructional text and hypothetical cases are original. Linked source readings supply published evidence where specified. Teachers should judge fit with their course and state requirements.