Conditions for Equilibrium (Cambridge (CIE) A Level Physics)

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

Step 3: Calculate the anticlockwise moments for each answer option

• For answer option C

Step 4: Determine if the beam is in equilibrium

clockwise moment = anticlockwise moment

• Therefore, beam C is in equilibrium

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

Which diagram correctly represents the forces acting at point X?

Answer:

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

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

Step 3: Check that the vectors form a closed path

• The correct answer is A

  • This is the only vector triangle forming a closed path

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