A-LevelPhysicsForces, density and pressure9702/21 · Oct/Nov 2017 · Q110 Marks
The drag force FD acting on a sphere moving through a fluid is given by the expression FD = Kρv² where K is a constant, ρ is the density of the fluid and v is the speed of the sphere.
- (a)Determine the SI base units of K.[3]
- (b)A ball of weight 1.5N falls vertically from rest in air. The drag force FD acting on the ball is given by the expression in (a). The ball reaches a constant (terminal) speed of 33ms⁻¹. Assume that the upthrust acting on the ball is negligible and that the density of the air is uniform. For the instant when the ball is travelling at a speed of 25ms⁻¹, determine
- (b)(i)the drag force FD on the ball,[2]
- (b)(ii)the acceleration of the ball.[2]
- (c)Describe the acceleration of the ball in (b) as its speed changes from zero to 33 ms⁻¹.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [C1] units of F: kgms⁻²
- [C1] units of ρ: kgm⁻³ and units of v: ms⁻¹
- [A1] units of K: kgms⁻² / [kgm⁻³ (ms⁻¹)²] = m²
- [C1] Kρ = 1.5/33² = 1.38 x 10⁻³
- [A1] FD = 1.38 × 10⁻³ × 25² or FD / 1.5 = 25²/33² FD = 0.86 N
- [C1] a = (1.5 – 0.86)/(1.5/9.81) or a = 9.81 – [0.86/ (1.5/9.81)]
- [A1] a = 4.2ms⁻²
- [B1] initial acceleration is g/9.81 (ms⁻²)/acceleration of free fall
- [B1] acceleration decreases
- [B1] final acceleration is zero
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