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Date	May 2017	Marks available	2	Reference code	17M.3.SL.TZ2.6
Level	Standard level	Paper	Paper 3	Time zone	2
Command term	Calculate	Question number	6	Adapted from	N/A

Question

A cylindrical space probe of mass 8.00 x 10² kg and diameter 12.0 m is at rest in outer space.

Rockets at opposite points on the probe are fired so that the probe rotates about its axis. Each rocket produces a force F = 9.60 x 10³ N. The moment of inertia of the probe about its axis is 1.44 x 10⁴ kg $\,$ m².

The diagram shows a satellite approaching the rotating probe with negligibly small speed. The satellite is not rotating initially, but after linking to the probe they both rotate together.

The moment of inertia of the satellite about its axis is 4.80 x 10³ kg $\,$ m². The axes of the probe and of the satellite are the same.

Deduce the linear acceleration of the centre of mass of the probe.

[1]

a.i.

Calculate the resultant torque about the axis of the probe.

[2]

a.ii.

The forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad $\,$ s^–1.

[2]

Determine the final angular speed of the probe–satellite system.

[2]

c.i.

Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.

[3]

c.ii.

Markscheme

zero

[1 mark]

a.i.

the torque of each force is 9.60 x 10³ x 6.0 = 5.76 x 10⁴ «Nm»

so the net torque is 2 x 5.76 x 10⁴ = 1.15 x 10⁵ «Nm»

Allow a one-step solution.

[2 marks]

a.ii.

the angular acceleration is given by $\frac{{1.15 \times {{10}^5}}}{{1.44 \times {{10}^4}}}$ «= 8.0 s^–2»

ω = « $\alpha$ t = 8.0 x 2.00 =» 16 «s^–1»

[2 marks]

1.44 x 10⁴ x 16.0 = (1.44 x 10⁴ + 4.80 x 10³) x ω

ω = 12.0 «s^–1»

Allow ECF from (b).

[2 marks]

c.i.

initial KE $\frac{1}{2} \times 1.44 \times {10^4} \times {16.0^2} = 1.843 \times {10^6}$ «J»

final KE $\frac{1}{2} \times \left( {1.44 \times {{10}^4} + 4.80 \times {{10}^3}} \right) \times {12.0^2} = 1.382 \times {10^6}$ «J»

loss of KE = 4.6 x 10⁵ «J»

Allow ECF from part (c)(i).

[3 marks]

c.ii.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

c.i.

[N/A]

c.ii.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.1 – Rigid bodies and rotational dynamics

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18N.3.SL.TZ0.6c.i:
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19N.3.SL.TZ0.5b(iii):
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17N.3.SL.TZ0.7d:
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18M.3.SL.TZ2.6a.i:
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18M.3.SL.TZ1.6c:
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19M.3.SL.TZ2.8b:
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20N.3.SL.TZ0.6a:
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17N.3.SL.TZ0.7e:
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20N.3.SL.TZ0.8:
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17M.3.SL.TZ2.6b:
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