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ASPhysicsCIERevision Notes4. Forces, Density & Pressure4.2 Equilibrium of ForcesConditions for Equilibrium

Conditions for Equilibrium (CIE AS Physics)

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Leander

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Leander

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Equilibrium

  • A system is in equilibrium when all the forces are balanced
    • There is no resultant force
    • There is no resultant torque

  • In accordance with Newton's First Law, an object in equilibrium will therefore remain at rest, or at a constant velocity, and will not rotate
  • The system is in an equilibrium state when applying the Principle of Moments 

Worked example

Four beams of the same length, each have three forces acting on them.

Which beam has both zero resultant force and zero resultant torque acting?

Answer:

Step 1: Consider the principle of moments

  • Zero resultant force and zero resultant torque mean that the beam is in equilibrium
  • Therefore, for the correct answer:

clockwise moment = anticlockwise moment

Step 2: Calculate the clockwise moments for each answer option

  • For answer option C
  • Taking the pivot to be the point at which the 15 N force acts
    • Therefore, there is no moment caused by the 15 N force because d = 0

clockwise space moment space equals space 40 space cross times space 0.5 space equals space 20 space straight N space straight m

Step 3: Calculate the anticlockwise moments for each answer option

  • For answer option C

anticlockwise space moment space equals space 25 space cross times space open parentheses 0.5 space plus space 0.3 close parentheses space equals space 20 space straight N space straight m

Step 4: Determine if the beam is in equilibrium

20 space straight N space straight m space equals space 20 space straight N space straight m

clockwise moment = anticlockwise moment

  • Therefore, beam C is in equilibrium

Coplanar forces in equilibrium

  • Coplanar forces can be represented by vector triangles
  • Forces are in equilibrium if an object is either
    • At rest
    • Moving at constant velocity

  • In equilibrium, coplanar forces are represented by closed vector triangles
    • The vectors, when joined together, form a closed path

  • The most common forces acting on objects are
    • Weight
    • Normal reaction force
    • Tension (from cords and strings)
    • Friction

Forming a vector triangle for forces acting on a body in equilibrium

Vector triangle in equilibrium, downloadable AS & A Level Physics revision notes

To form a closed vector triangle, draw a free-body force diagram, then rearrange the force arrows tip to tail maintaining the length and directions of the vectors

 

Worked example

A mass hangs in equilibrium from a cable at point X. The tensions in the cables are T1 and T2 as shown.

WE - Forces in equilibrium question image 1, downloadable AS & A Level Physics revision notesWhich diagram correctly represents the forces acting at point X?WE - Forces in equilibrium question image 2, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Draw a free-body force diagram identifying the direction of all the forces

4-2-2-equilibrium-we-step1-cie-new

Step 2: Arrange the vectors into a triangle, maintaining the magnitudes and directions

4-2-2-equilibrium-we-step2-cie-new

Step 3: Check that the vectors form a closed path

4-2-2-equilibrium-we-step3-cie-new

  • The correct answer is A
    • This is the only vector triangle forming a closed path

Examiner Tip

The diagrams in exam questions about this topic tend to be drawn to scale, so make sure you have a ruler handy!

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    Leander

    Author: Leander

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.