Forces, Rotation & Equilibrium — Extension · Physics & Environmental Science, Grade 12
Use force diagrams, friction, circular motion, springs, and torque to explain motion and balance.
Spring Force and Torque Evidence
Investigate
Does force scale with extension and does a lever balance by torque?
Use two dedicated sessions: first define the model, boundary, variables and comparison, then collect suitable records or analyze the complete supplied-data route; second complete calculations/graphs, compare alternatives, revise and prepare the report. Extend collection time where needed. Supplied-data work does not certify supervised laboratory minutes or mandated investigations.
Materials
- Notebook, graph paper, and calculator
- The supplied data table is sufficient for analysis
- Optional household setup described in the method; an adult checks safety
Before you begin
Use only the listed household materials or analyze the supplied data. An adult should review setup. No flames, strong acids/alkalis, unknown chemicals, household mains, radiation sources, or high-speed projectiles are needed. Keep food-study materials separate from eating and wash hands afterward.
Plan a fair test
Use one spring within a gentle elastic range. Change extension and record force; evaluate a separate ideal lever diagram.
Method
- Write a prediction and the mechanism that supports it.
- Draw the setup or boundary; label axes, quantities, and units.
- Plot force against extension and estimate the line slope.
- Find spring energy from the area under the graph.
- Balance a 6 N load at 0.20 m with an opposite force at 0.60 m; include a support force in the force diagram.
- Record independent repetitions where possible, raw values, and instrument resolution.
- Write a claim citing numerical evidence, a limitation, and a follow-up test.
Example data — for analysis when materials are unavailable
Illustrative teaching data, not measurements from a real district laboratory. Analyze these when materials are unavailable and identify them as provided data. Do not claim to have performed a measurement you did not make.
| Extension (m) | Force (N) |
|---|---|
| 0.01 | 1 |
| 0.02 | 2 |
| 0.03 | 3 |
Analyze and explain
- Find stiffness and energy at 0.03 m.
- Find input force for the ideal lever.
- What evidence would reject the linear spring model?
- Link the pattern to a labeled particle, structure, energy or amount model from the chapter.
- Distinguish supplied illustrative records from measurements actually collected.
- Identify uncertainty and propose a comparison that would test an alternative explanation.
What a strong explanation includes
- A stated prediction, conditions, and controlled variables or explicit model boundary.
- A labeled table/graph with units, calculations, and attention to repeated values or uncertainty.
- A claim citing numerical evidence and a scientifically accurate mechanism.
- A limitation, alternative explanation, and useful follow-up test.
- Preserve initial reasoning and an evidence-supported revision.
- Check units, object/material identity, system boundary and physical assumptions.
Parent / teacher guide: discuss after the investigation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Compare this model with the learner’s actual evidence. Different measurements can support a different conclusion; check the reasoning and limitations, not matching wording.
Extend the chapter investigation by evaluating its evidence and proposing a better test.
Problem 1
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Problem 2
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Problem 3
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Problem 4
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Problem 5
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.
Problem 6
Answer and explanation
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model. Preserve the original observations, intermediate working and a labeled mechanism. Report the relevant boundary and model assumptions, discuss an alternative explanation, and identify the next useful measurement; do not replace unexpected data with the illustrative record.