Sketch on figure 2 the variation of the total energy

Sketch, on Figure 2 , the variation of the total energy of the mass – spring system
with displacement.
[2 marks]
Question 1 continues on the next page

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Spring X is replaced with an elastic string Y that obeys Hooke’s law.
Figure 3 shows the load attached to the end of Y .
Y has negligible mass.
Y has an extension of
42 mm
when the load is at rest in its equilibrium position.
Figure 3
0 1 . 3 The load is pulled
20 mm
vertically downwards below its equilibrium position.
It is then released and oscillates with SHM.
Show that the period of the oscillations is approximately
0.4 s
.
[2 marks]
The load on Y is now pulled
50 mm
vertically downwards below its equilibrium position
and released.
The movement of the load fulfils the conditions for SHM until the load reaches a
position P . When the load is at P , the elastic string Y is at its unstretched length.
0 1 . 4 Calculate the velocity of the load at P .
[3 marks]
velocity
= m s
–1

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0 1
. 5 The load continues to move upwards after reaching P .
Explain why this movement above P does not fulfil the conditions for SHM.
[2 marks]
0 1
. 6 State whether spring X or elastic string Y has the greater stiffness.
Explain your answer.
[2 marks]
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0 2 Drinking water is taken from an underground lake.
The water contains small quantities of radioactive isotopes such as tritium
( )
3
H
1
.
The decay of tritium has a half-life of
12.3
years.
0 2
. 1 Water is unsafe to drink when its activity due to tritium decay is greater
than
7.6 × 10
7
Bq
per cubic metre of water.
2.50 × 10
− 4
m
3
of water from the lake contains
1.1 × 10
10
tritium atoms.
Deduce whether the amount of tritium in water from this lake makes it unsafe to drink.
[3 marks]
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IB/M/Jan22/PH03