User interface language: English | Español

Date November 2020 Marks available 1 Reference code 20N.2.HL.TZ0.7
Level Higher level Paper Paper 2 Time zone 0 - no time zone
Command term Outline Question number 7 Adapted from N/A

Question

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=-ρAgx

where ρ is the density of water.

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

Outline why the cylinder performs simple harmonic motion when released.

[1]
a.

The mass of the cylinder is 118kg and the cross-sectional area of the cylinder is 2.29×10-1m2. The density of water is 1.03×103kgm-3. Show that the angular frequency of oscillation of the cylinder is about 4.4rads-1.

[2]
b.

Determine the maximum kinetic energy Ekmax of the cylinder.

[2]
c(i).

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]
c(ii).

Markscheme

the «restoring» force/acceleration is proportional to displacement


Allow use of symbols i.e.
F-x or a-x

a.

Evidence of equating mω2x=ρAgx «to obtain ρAgm=ω2» ✓

 

ω=1.03×103×2.29×10-1×9.81118 OR 4.43«rads-1» ✓

 

Answer to at least 3 s.f.

b.

«EK is a maximum when x=0 hence» EK, max=12×118×4.420.2502-02 


71.4 «J»

c(i).

energy never negative

correct shape with two maxima

c(ii).

Examiners report

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

a.

Again, very well answered.

b.

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

c(i).

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

c(ii).

Syllabus sections

Core » Topic 4: Waves » 4.1 – Oscillations
Show 38 related questions
Core » Topic 4: Waves
Core

View options