A-Level Physics May/June 2024 Q2(b): The mass of the skydiver and her equipment is 68kg. The upthrust on the skydiver is neg…

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  To find the acceleration, we must first find the resultant force acting on the skydiver using Newton's Second Law, $F_{net} = ma$.

  Let's define the downward direction as positive.

  1. Calculate the weight (force due to gravity): $W = mg$ $W = 68 \text{ kg} \times 9.81 \text{ m/s}^2 = 667.08 \text{ N}$ (downwards)

  2. Identify the forces and find the net force: The forces are weight ($W$) acting downwards (+667.08 N) and drag ($D$) acting upwards (-1800 N). $F_{net} = W - D$ $F_{net} = 667.08 \text{ N} - 1800 \text{ N} = -1132.92 \text{ N}$

  3. Calculate the acceleration: $a = \frac{F_{net}}{m}$ $a = \frac{-1132.92 \text{ N}}{68 \text{ kg}} = -16.66... \text{ m/s}^2$

  The magnitude of the acceleration is $17 \text{ m/s}^2$ (to 2 s.f.). The negative sign indicates the direction is opposite to our positive (downward) direction, so the acceleration is upwards.

  acceleration = ..........$17$.......... ms⁻² direction = ..........upwards..........

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  How the marks are awarded

  • C1 — Correctly calculating the resultant force by finding the difference between the weight and the drag force, as shown by the working 68 × 9.81 – 1800.
  • A1 — Correctly applying Newton's second law ($a = F/m$) to find the acceleration, dividing the resultant force by the mass to get an answer of 17 m/s² or 16.7 m/s².
  • B1 — Correctly stating the direction of the acceleration as 'upwards'.

  Common mistakes

  • Adding the weight and drag force instead of subtracting them, failing to recognise they are in opposite directions.
  • Calculating the resultant force correctly but then stating the direction is 'downwards', not realising the net force is upwards.
  • Ignoring the weight of the skydiver and calculating acceleration using only the drag force (e.g., a = 1800 / 68).
  • Making a sign convention error, leading to confusion about the final direction of acceleration.

  Examiner tip: Always start dynamics problems by drawing a simple free-body diagram and defining a positive direction to correctly determine the resultant force.

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