DP Physics (last assessment 2024)

Question 20N.2.HL.TZ0.7b

Date	November 2020	Marks available	[Maximum mark: 2]	Reference code	20N.2.HL.TZ0.7b
Level	HL	Paper	2	Time zone	TZ0
Command term	Show that	Question number	b	Adapted from	N/A

[Maximum mark: 2]

20N.2.HL.TZ0.7b

A vertical solid cylinder of uniform cross-sectional area $A$ floats in water. The cylinder is partially submerged. When the cylinder floats at rest, a mark is aligned with the water surface. The cylinder is pushed vertically downwards so that the mark is a distance $x$ below the water surface.

At time $t = 0$ the cylinder is released. The resultant vertical force $F$ on the cylinder is related to the displacement $x$ of the mark by

$F = - ρ A g x$

where $ρ$ is the density of water.

(b)

The mass of the cylinder is $118 kg$ and the cross-sectional area of the cylinder is $2.29 \times 10^{- 1} m^{2}$ . The density of water is $1.03 \times 10^{3} kg m^{- 3}$ . Show that the angular frequency of oscillation of the cylinder is about $4.4 rad s^{- 1}$ .

[2]

Markscheme

Evidence of equating $m ω^{2} x = ρ A g x$ «to obtain $\frac{ρ A g}{m} = ω^{2}$ » ✓

$ω = \sqrt{\frac{1.03 \times 10^{3} \times 2.29 \times 10^{- 1} \times 9.81}{118}}$ OR $4.43 « rad s^{- 1} »$ ✓

Answer to at least $3$ s.f.

Examiners report

Again, very well answered.

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Additional higher level (AHL)

Additional higher level (AHL) » Topic 9: Wave phenomena » 9.1 – Simple harmonic motion

Additional higher level (AHL) » Topic 9: Wave phenomena

Question 20N.2.HL.TZ0.7b

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