Springs, Torque & Static Equilibrium — Practice · Grade 12 Science

Chapter: Forces, Rotation & Equilibrium

What this practice covers

By the end of Springs, Torque & Static Equilibrium you should be able to:

9 questions, numeric and written answer, each with a worked explanation.

Vocabulary used: spring constant, torque, lever arm.

Problem 1

k=100N/m,x=.03 m. Find force magnitude.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

3 N

100×.03=3.

Problem 2

Why can zero net force still permit rotation?
Answer and explanation

The force lines can produce a nonzero net torque about the object.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 3

Find spring energy for k=200 N/m and x=.10 m.
Hints

List the given quantities, select a relationship, and check units before substituting.

Answer and explanation

1 J

½×200×.10²=1.

Problem 4

Why is spring work not final force times extension?
Answer and explanation

Force varies with extension; integrate or use the triangular graph area.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

A spring of k=200 N/m is stretched 0.05 m within its linear range. Find force magnitude. Show the reasoning, not just the conclusion.
Hints

Use perpendicular lever arm and rotational sign.

Answer and explanation

F=kx=10 N, directed toward restoring equilibrium.

Problem 6

Why does static equilibrium require both zero net force and zero net torque?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

Zero net force prevents translational acceleration; zero net torque prevents angular acceleration.

Problem 7

Static equilibrium requires force and torque balanceStatic equilibrium requires force and torque balance30 N at 0.30 m30 N at 0.30 msupport 60 NΣF=0 and Στ=0 are both required.
Original symmetric weightless-bar model; distributed bar weight is intentionally excluded here.
Interpret the supplied visual. Could a zero-torque calculation alone establish static equilibrium?
Answer and explanation

No. The vector force sum must also vanish, and the starting state must be at rest.

Static equilibrium means the body remains at rest without translational or rotational acceleration. It needs ΣF=0 and Στ=0 about a selected pivot in the rigid-body model. Equal opposing torques alone can coexist with nonzero net force, while balanced forces can still form a turning couple. For this weightless-bar example equal downward loads at equal opposite arms balance torque, and the upward support must balance their combined 60 N force.

No. The vector force sum must also vanish, and the starting state must be at rest.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 8

A weightless 2 m beam is pivoted at its left end. A 60 N load acts 0.50 m from the pivot. An upward force acts at the right end. Find that force and vertical pivot reaction for equilibrium.
Answer and explanation

Torque balance: F×2=60×0.50, so F=15 N upward. Vertical balance gives pivot reaction=60−15=45 N upward. Both balances are necessary.

Torque balance: F×2=60×0.50, so F=15 N upward.

Vertical balance gives pivot reaction=60−15=45 N upward.

Both balances are necessary.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 9

OpenSciEd drawing of six cushioning rings arranged in a triangle with a broad base on the table and one top ring touching the loaded plate.
The source arrangement shows rings supporting a plate/load; it contains no quantitative force–time or force–extension record. Triangular stack of cushioning rings · OpenSciEd · 8.1 Contact Forces, Lesson 13, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.
Select the loaded plate as the body. Name its vertical forces at rest, identify the support force’s third-law partner and explain why this drawing alone cannot establish impact peak force.
Answer and explanation

The rings push the loaded plate upward and Earth attracts that selected plate/load downward. Their magnitudes balance at rest but they are not a third-law pair. The plate pushes the rings downward as the support force’s partner on a different body. Impact peak force requires a time-resolved interaction and motion record, not a static layout.

Read source labels, scope, axes and intentional omissions.

Use the complete local explanation to draw a justified mechanism or calculate a supported quantity.

State what is observed, what is assumed and what evidence remains needed.

Response criteria

  • Interpret the source labels, units and scope accurately.
  • Explain the relevant mechanism with a labeled model or supported calculation.
  • Identify a meaningful assumption, uncertainty or missing comparison.

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