AQA AS Level Physics Paper 1, June 2019: Question 5

✅ Correct Answer

0.56 N (or half the total weight since the system is symmetrical)

📐 Calculation Steps

1. Recognise that because the meter rule is uniform and supported symmetrically at 12.0 cm from each end, forces A and B share the total weight equally.
2. Calculation: Total weight = 1.12 N. Reading on A = 1.12 / 2 = 0.56 N .

✅ Correct Answer

The student's suggestion is incorrect. Although forces A and B are equal in magnitude, they act in the same direction (upwards), whereas a couple requires two equal, parallel forces acting in opposite directions.

💡 Key Knowledge

• Definition of a couple: A pair of equal and opposite coplanar forces.
• A couple produces rotation without translation, and its moment is independent of the pivot point. Forces A and B here combine to cause translational equilibrium (balancing total downward weight).

❌ Common Errors

Students often mistake any pair of equal forces in a setup for a couple, forgetting the strict requirement that they must act in opposite directions.

✅ Correct Answer

W = 0.32 N and d = 0.14 m (or 14 cm)

📐 Step-by-Step Calculation

1. Find W using resolution of vertical forces:
   Total upward force = Total downward force
   Reading A + Reading B = Weight of ruler + W
   0.82 + 0.62 = 1.12 + W
   1.44 = 1.12 + W  ⇒  W = 0.32 N
2. Find distance d using the Principle of Moments:
   Take moments about the pivot point at support A to eliminate unknown reaction forces:
   Clockwise moments = Anticlockwise moments
   (W × d) + (Weight of ruler × distance from A to center of mass)
   *Note: Ruler is 100 cm long. Support A is at 12.0 cm. Center of mass is at 50.0 cm.*
   Distance from A to center of mass = 50.0 - 12.0 = 38.0 cm (0.38 m).
   Anticlockwise moment about A = Support B force × distance from A to B.
   Distance from A to B = 100.0 - 12.0 (left end offset) - 12.0 (right end offset) = 76.0 cm (0.76 m).
3. Set up moment equation about A:
   (W × d) + (1.12 × 0.38) = 0.62 × 0.76
   (0.32 × d) + 0.4256 = 0.4712
   0.32 × d = 0.0456  ⇒  d = 0.1425 m ≈ 0.14 m

🧠 Exam Technique

Always take moments about a point where an unknown force acts (like support A) to eliminate it from your calculations. Make sure to convert all centimeter distances into meters consistently to avoid powers-of-ten errors.

✅ Correct Answer

The readings on A and B would be different from question 05.3 (specifically, they would each be 0.72 N, totaling 1.44 N).

💡 Key Knowledge

• The total downward force (weight of ruler + W) remains constant at 1.44 N. Therefore, the sum of the vertical upward forces must still equal 1.44 N.
• Because the mass is in the exact same position relative to the ruler, the symmetry of the total downward load distribution means supports A and B will share the 1.44 N load equally if the new angle changes perpendicular distances by the same scaling factor (cos θ).

❌ Common Errors

Many students incorrectly assume that tilting the ruler changes the total weight acting downwards or alters the reaction forces unpredictably, forgetting that translational equilibrium in the vertical plane (ΣF = 0) still strictly applies.