A-LevelPhysicsForces, density and pressure9702/22 · Feb/Mar 2017 · Q17 Marks

A floating sphere is attached by a cable to the bottom of a river, as shown in [Figure 1.2]. The sphere is in equilibrium, with the cable at an angle of 75° to the horizontal. Assume that the force on the sphere due to the water flow is in the horizontal direction. The radius of the sphere is 23 cm. The sphere is solid and is made from a material of density 82 kg m⁻³.

(a)Complete Fig. 1.1 by putting a tick (√) in the appropriate column to indicate whether the listed quantities are scalars or vectors. quantity | scalar | vector ---|---|--- acceleration | | force | | kinetic energy | | momentum | | power | | work | | [Figure 1.1][2]
(b)(i)Show that the weight of the sphere is 41 N.[2]
(b)(ii)The tension in the cable is 290 N. Determine the upthrust acting on the sphere.[2]
(b)(iii)Explain the origin of the upthrust acting on the sphere.[1]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[A1] (a) scalars: kinetic energy, power, work
[A1] (a) vectors: acceleration, force, momentum
[C1] (b)(i) mass = volume × density or m = V × ρ
[C1] (b)(i) = 4/3 π (23 × 10⁻²)³ × 82
[A1] (b)(i) weight = 4/3 π (23 × 10⁻²)³ × 82 × 9.8 = 41 N
[C1] (b)(ii) vertical component of tension = 290 sin75° or 290 cos15° (= 280)
[A1] (b)(ii) upthrust = 290 sin75° + 41 = 320 (321) N
[B1] (b)(iii) the water pressure is greater than the air pressure OR the pressure on lower surface (of sphere) is greater than the pressure on upper surface (of sphere)

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