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Date May 2017 Marks available 2 Reference code 17M.2.HL.TZ1.7
Level Higher level Paper Paper 2 Time zone 1
Command term Describe Question number 7 Adapted from N/A

Question

A student is investigating a method to measure the mass of a wooden block by timing the period of its oscillations on a spring.

A 0.52 kg mass performs simple harmonic motion with a period of 0.86 s when attached to the spring. A wooden block attached to the same spring oscillates with a period of 0.74 s.

With the block stationary a longitudinal wave is made to travel through the original spring from left to right. The diagram shows the variation with distance x of the displacement y of the coils of the spring at an instant of time.

A point on the graph has been labelled that represents a point P on the spring.

Describe the conditions required for an object to perform simple harmonic motion (SHM).

[2]
a.

Calculate the mass of the wooden block.

[2]
b.

In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.

[3]
c.

A second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.

[3]
d.

State the direction of motion of P on the spring.

[1]
e.i.

Explain whether P is at the centre of a compression or the centre of a rarefaction.

[2]
e.ii.

Markscheme

acceleration/restoring force is proportional to displacement
and in the opposite direction/directed towards equilibrium

a.

ALTERNATIVE 1

T21T22=m1m2T21T22=m1m2

mass = 0.38 / 0.39 «kg»

 

ALTERNATIVE 2

«use of =2πmk=2πmk» k = 28 «Nm–1»

«use of =2πmk=2πmk» m = 0.38 / 0.39 «kg»

 

Allow ECF from MP1.

b.

ω = «2π0.742π0.74» = 8.5 «rads–1»

total energy = 12×0.39×8.52×(4.8×102)212×0.39×8.52×(4.8×102)2

= 0.032 «J»

 

Allow ECF from (b) and incorrect ω.

Allow answer using k from part (b).

c.

spring constant/k/stiffness would increase
T would be smaller
fractional uncertainty in T would be greater, so fractional uncertainty of mass of block would be greater

d.

left

e.i.

coils to the right of P move right and the coils to the left move left

hence P at centre of rarefaction

 

Do not allow a bald statement of rarefaction or answers that don’t include reference to the movement of coils.

Allow ECF from MP1 if the movement of the coils imply a compression.

e.ii.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.i.
[N/A]
e.ii.

Syllabus sections

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