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Date	November 2020	Marks available	2	Reference code	20N.3.HL.TZ0.12
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Determine	Question number	12	Adapted from	N/A

Question

A sphere is dropped into a container of oil.
The following data are available.

Density of oil $= 915 kg m^{- 3}$
Viscosity of oil $= 37.9 \times 10^{- 3} Pas$
Volume of sphere $= 7.24 \times 10^{- 6} m^{3}$
Mass of sphere $= 12.6 g$

The sphere is now suspended from a spring so that the sphere is below the surface of the oil.

State two properties of an ideal fluid.

[2]

Determine the terminal velocity of the sphere.

[3]

Determine the force exerted by the spring on the sphere when the sphere is at rest.

[2]

c(i).

The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by $10 %$ . Calculate the $Q$ factor for this system.

[1]

c(ii).

Outline the effect on $Q$ of changing the oil to one with greater viscosity.

[2]

c(iii).

Markscheme

incompressible ✓

non-viscous ✓

laminar/streamlined flow ✓

radius of sphere $= 0.012 « m »$ ✓

weight of sphere $= 6 π η r v + ρ V g$

$v = \frac{(1.26 \times 10^{- 2} - 915 \times 7.24 \times 10^{- 6}) \times 9.81}{6 π \times 37.9 \times 10^{- 3} \times 1.2 \times 10^{- 2}}$ ✓

$v = 6.84 « m s^{- 1} »$ ✓

Accept use of $g = 10$ leading to $v = 7.0 « m s^{- 1} »$

Allow implicit calculation of radius for MP1

Do not allow ECF for MP3 if buoyant force omitted.

$F = m g - ρ V g$

$F = (0.0126 \times 9.81) - (915 \times 7.24 \times 10^{- 6} \times 9.81)$ ✓

$F = 5.86 \times 10^{- 2} « N »$ ✓

Accept use of $g = 10$ leading to $F = 6.0 \times 10^{- 2} N$

c(i).

$Q = « 2 π \times \frac{energy stored}{energy lost} = 2 π \times \frac{100}{10} = » 63$ ✓

c(ii).

drag force increases OR damping increases OR more energy lost per cycle ✓

$Q$ will decrease ✓

c(iii).

Examiners report

The properties of fluids proved to be a very well-studied topic.

Only those candidates who forgot to include the buoyant force missed marks here.

Continuing from b, most candidates scored full marks.

c(i).

The calculation needed to obtain the Q-factor proved to be known by many.

c(ii).

Very well answered.

c(iii).

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.3 – Fluids and fluid dynamics (HL only)

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Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics)

Option B: Engineering physics

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