DP Physics (last assessment 2024)

Question 20N.2.HL.TZ0.c(i)

Date	November 2020	Marks available	[Maximum mark: 2]	Reference code	20N.2.HL.TZ0.c(i)
Level	HL	Paper	2	Time zone	TZ0
Command term	Determine	Question number	c(i)	Adapted from	N/A

c(i).

[Maximum mark: 2]

20N.2.HL.TZ0.c(i)

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.

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

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

[2]

Markscheme

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