DP Physics (last assessment 2024)

Question 20N.2.HL.TZ0.7

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

[Maximum mark: 7]

20N.2.HL.TZ0.7

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.

(a)

Outline why the cylinder performs simple harmonic motion when released.

[1]

Markscheme

the «restoring» force/acceleration is proportional to displacement ✓

Allow use of symbols i.e. $F \propto - x$ or $a \propto - x$

Examiners report

This was well answered with candidates gaining credit for answers in words or symbols.

(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.

The cylinder was initially pushed down a distance $x = 0.250 m$ .

(c(i))

Determine the maximum kinetic energy $E_{kmax}$ of the cylinder.

[2]

Markscheme

« $E_{K}$ is a maximum when $x = 0$ hence» $E_{K, \max} = \frac{1}{2} \times 118 \times 4 . 4^{2} (0 . 250^{2} - 0^{2})$ ✓

$71.4 « J »$ ✓

Examiners report

A straightforward calculation with the most common mistake being missing the squared on the omega.

(c(ii))

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$ .

[2]

Markscheme

energy never negative ✓

correct shape with two maxima ✓

Examiners report

Most candidates answered with a graph that was only positive so scored the first mark.

Syllabus sections

Core

Core » Topic 4: Waves » 4.1 – Oscillations

Core » Topic 4: Waves

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.TZ0.7

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