A-Level Physics May/June 2025 Q2(b)(i): By taking moments about point Q, show that θ is 25°.

1 answer

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  According to the principle of moments, for an object in rotational equilibrium, the sum of the clockwise moments about a pivot must equal the sum of the anticlockwise moments about the same pivot.

  Taking moments about point Q:

  Sum of clockwise moments ($M_{CW}$) = Moment from the weight of the sign $M_{CW} = \text{Force} \times \text{Perpendicular distance}$ $M_{CW} = (270 \times 9.81) \times 1.2$ $M_{CW} = 3178.44 \text{ Nm}$

  Sum of anticlockwise moments ($M_{ACW}$) = Moment from the tension in the post support From the geometry of the forces acting on the post: $M_{ACW} = 1800 \times \frac{1.6}{\cos\theta}$ $M_{ACW} = \frac{2880}{\cos\theta}$

  For equilibrium, $M_{CW} = M_{ACW}$: $3178.44 = \frac{2880}{\cos\theta}$

  Rearranging to solve for $\theta$: $\cos\theta = \frac{2880}{3178.44}$ $\cos\theta = 0.90610...$ $\theta = \cos^{-1}(0.90610...)$ $\theta = 25.02...^\circ$

  Therefore, to two significant figures, $\theta$ is $25^\circ$.

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  How the marks are awarded

  • B1 — Correctly writing the expression for the clockwise moment due to the sign's weight, by multiplying the weight (270 × 9.81 N) by its perpendicular distance from pivot Q (1.2 m).
  • B1 — Correctly writing the expression for the anticlockwise moment in terms of θ, which is given as 1800 × (1.6 / cosθ).
  • B1 — Equating the clockwise and anticlockwise moments and carrying out the calculation to show that θ is 25°. This includes correctly rearranging the equation and finding the value of θ before rounding.

  Common mistakes

  • Using the mass (270 kg) instead of the weight (270 × 9.81 N) when calculating the moment, leading to an incorrect value for θ.
  • Making a trigonometric error when determining the expression for the anticlockwise moment, for example using sinθ or multiplying by cosθ instead of dividing.
  • Incorrectly rearranging the final equation, for instance calculating cosθ = (Clockwise moment) / 2880 instead of 2880 / (Clockwise moment).
  • In a 'show that' question, failing to show the final calculated value (e.g., 25.02°) before rounding to the value given in the question (25°).

  Examiner tip: For any equilibrium problem, always start by drawing a clear diagram showing all forces and their perpendicular distances from the chosen pivot point.

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