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Date	May 2019	Marks available	2	Reference code	19M.2.HL.TZ1.6
Level	Higher level	Paper	Paper 2	Time zone	1
Command term	Show that	Question number	6	Adapted from	N/A

Question

A small metal pendulum bob is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible.

The pendulum begins to oscillate. Assume that the motion of the system is simple harmonic, and in one vertical plane.

The graph shows the variation of kinetic energy of the pendulum bob with time.

When the 75 g bob is moving horizontally at 0.80 m s^–1, it collides with a small stationary object also of mass 75 g. The object and the bob stick together.

Calculate, in m, the length of the thread. State your answer to an appropriate number of significant figures.

[3]

a.i.

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

[1]

a.ii.

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

[2]

a.iii.

Calculate the speed of the combined masses immediately after the collision.

[1]

b.i.

Show that the collision is inelastic.

[3]

b.ii.

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

[2]

b.iii.

The speed after the collision of the bob and the object was measured using a sensor. This sensor emits a sound of frequency f and this sound is reflected from the moving bob. The sound is then detected by the sensor as frequency f′.

Explain why f and f′ are different.

[3]

b.iv.

Markscheme

identifies T as 2.25 s ✔

L = 1.26 m ✔

1.3 / 1.26 «m» ✔

Accept any number of s.f. for MP2.

Accept any answer with 2 or 3 s.f. for MP3.

a.i.

X labels any point on the curve where E_K $\frac{1}{4}$ of maximum/5 mJ ✔

a.ii.

$\frac{1}{2}$ mv² = 20 × 10⁻³ seen OR $\frac{1}{2}$ × 7.5 × 10^-2 × v² = 20 × 10^-3 ✔

0.73 «m s⁻¹» ✔

Must see at least 2 s.f. for MP2.

a.iii.

0.40 «m s^-1» ✔

b.i.

initial energy 24 mJ and final energy 12 mJ ✔

energy is lost/unequal /change in energy is 12 mJ ✔

inelastic collisions occur when energy is lost ✔

b.ii.

graph with same period but inverted ✔

amplitude one half of the original/two boxes throughout (by eye) ✔

b.iii.

mention of Doppler effect ✔

there is a change in the wavelength of the reflected wave ✔

because the wave speed is constant, there is a change in frequency ✔

b.iv.

Examiners report

This question was well approached by candidates. The noteworthy mistakes were not reading the correct period of the pendulum from the graph, and some simple calculation and mathematical errors. This question also had one mark for writing an answer with the correct number of significant digits. Candidates should be aware to look for significant digit question on the exam and can write any number with correct number of significant digits for the mark.

a.i.

[N/A]

a.ii.

This question was well answered. This is a “show that” question so candidates needed to clearly show the correct calculation and write an answer with at least one significant digit more than the given answer. Many candidates failed to appreciate that the energy was given in mJ and the mass was in grams, and that these values needed to be converted before substitution.

a.iii.

[N/A]

b.i.

Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.

b.ii.

Many candidates drew graphs that received one mark for either recognizing the phase difference between the gravitational potential energy and the kinetic energy, or for recognizing that the total energy was half the original energy. Few candidates had both features for both marks.

b.iii.

This question was essentially about the Doppler effect, and therefore candidates were expected to give a good explanation for why there is a frequency difference. As with all explain questions, the candidates were required to go beyond the given information. Very few candidates earned marks beyond just recognizing that this was an example of the Doppler effect. Some did discuss the change in wavelength caused by the relative motion of the bob, although some candidates chose very vague descriptions like “the waves are all squished up” rather than using proper physics terms. Some candidates simply wrote and explained the equation from the data booklet, which did not receive marks. It should be noted that this was a three mark question, and yet some candidates attempted to answer it with a single sentence.

b.iv.

Syllabus sections

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

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