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AS · Practice questions · Equilibrium of forces

Balance the forces and the moments.

Six original Cambridge-style questions on the principle of moments, finding reaction forces on beams, the two conditions for equilibrium, and a three-force vector triangle.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Two conditions, one method.

01
Analysis
[2 marks]

State the two conditions that must both be satisfied for a body to be in equilibrium under a system of coplanar forces.

  • The resultant force in any direction is zero. ✓
  • The resultant moment about any point is zero. ✓
02
Analysis
[3 marks]

A uniform metre rule of weight 1.2 N is pivoted at the 30 cm mark. A weight is hung at the 10 cm mark to balance it. Find the weight needed. (The rule's weight acts at the 50 cm mark.)

  • The rule's weight acts at 50 cm, which is 20 cm to the right of the pivot: clockwise moment = 1.2 × 0.20 = 0.24 N m. ✓
  • The hung weight is at 10 cm, 20 cm to the left: anticlockwise moment = W × 0.20. ✓
  • Balance: W × 0.20 = 0.24, so W = 1.2 N. ✓
03
Analysis
[3 marks]

A uniform beam of weight 80 N and length 6.0 m rests horizontally on two supports, one at each end. A 120 N load is placed 2.0 m from the left support. By taking moments about the left support, find the upward force at the right support.

  • Moments about the left support: R × 6.0 = (80 × 3.0) + (120 × 2.0). ✓
  • R × 6.0 = 240 + 240 = 480, so R = 80 N. ✓
  • (The left support then carries 80 + 120 − 80 = 120 N.) ✓
04
Analysis
[3 marks]

A 50 N picture hangs from a single nail by two wires that each make 50° with the horizontal. Find the tension in each wire.

  • Vertical balance: 2T sin 50° = 50. ✓
  • 2T × 0.766 = 50, so 1.532T = 50. ✓
  • T = 33 N in each wire. ✓
05
Analysis
[2 marks]

Explain why a pair of equal and opposite forces that are not in the same line is not in equilibrium, even though the resultant force is zero.

  • The resultant force is zero, so the first condition is met. ✓
  • But the forces form a couple with a non-zero resultant moment, so there is a turning effect and the second condition fails: it is not in equilibrium. ✓
06
Analysis
[3 marks]

A street lamp of weight 200 N is held out from a wall by a horizontal rod, with a wire from the wall to the end of the rod making 35° above the rod. Treating the lamp as hanging from the end of the rod, find the tension in the wire. (The wire's vertical component supports the lamp.)

  • The wire's vertical component must balance the lamp's weight: T sin 35° = 200. ✓
  • T × 0.574 = 200, so T = 200 / 0.574. ✓
  • T = 350 N (to 2 significant figures). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.