| Date | May 2017 | Marks available | 2 | Reference code | 17M.2.HL.TZ1.7 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Explain | 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).
Calculate the mass of the wooden block.
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.
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.
State the direction of motion of P on the spring.
Explain whether P is at the centre of a compression or the centre of a rarefaction.
Markscheme
acceleration/restoring force is proportional to displacement
and in the opposite direction/directed towards equilibrium
ALTERNATIVE 1
\(\frac{{T_1^2}}{{T_2^2}} = \frac{{{m_1}}}{{{m_2}}}\)
mass = 0.38 / 0.39 «kg»
ALTERNATIVE 2
«use of T \( = 2\pi \sqrt {\frac{m}{k}} \)» k = 28 «Nm–1»
«use of T \( = 2\pi \sqrt {\frac{m}{k}} \)» m = 0.38 / 0.39 «kg»
Allow ECF from MP1.
ω = «\(\frac{{2\pi }}{{0.74}}\)» = 8.5 «rads–1»
total energy = \(\frac{1}{2} \times 0.39 \times {8.5^2} \times {(4.8 \times {10^{ - 2}})^2}\)
= 0.032 «J»
Allow ECF from (b) and incorrect ω.
Allow answer using k from part (b).
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
left
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.
