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Date	November 2018	Marks available	2	Reference code	18N.2.SL.TZ0.1
Level	Standard level	Paper	Paper 2	Time zone	0 - no time zone
Command term	Estimate	Question number	1	Adapted from	N/A

Question

Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

The mass of ions ejected each second is 6.6 × 10^–6kg and the speed of each ion is 5.2 × 10⁴ m s^–1. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.

An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.

In practice, the ions leave the spacecraft at a range of angles as shown.

On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.

Determine the initial acceleration of the spacecraft.

[2]

Estimate the maximum speed of the spacecraft.

[2]

b.i.

Outline why scientists sometimes use estimates in making calculations.

[1]

b.ii.

Outline why the ions are likely to spread out.

[2]

c.i.

Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.

[2]

c.ii.

Outline what is meant by the gravitational field strength at a point.

[2]

d.i.

Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.

[1]

d.ii.

Markscheme

change in momentum each second = 6.6 × 10⁻⁶ × 5.2 × 10⁴ «= 3.4 × 10⁻¹kg m s⁻¹» ✔

acceleration = « $\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}$ =» 4.6 × 10⁻⁴ «m s⁻²» ✔

ALTERNATIVE 1:

(considering the acceleration of the spacecraft)

time for acceleration = $\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}$ = «4.6 × 10⁶» «s» ✔

max speed = «answer to (a) × 4.6 × 10⁶ =» 2.1 × 10³ «m s⁻¹» ✔

ALTERNATIVE 2:

(considering the conservation of momentum)

(momentum of 30 kg of fuel ions = change of momentum of spacecraft)

30 × 5.2 × 10⁴= 710 × max speed ✔

max speed = 2.2 × 10³«m s⁻¹» ✔

b.i.

problem may be too complicated for exact treatment ✔

to make equations/calculations simpler ✔

when precision of the calculations is not important ✔

some quantities in the problem may not be known exactly ✔

b.ii.

ions have same (sign of) charge ✔

ions repel each other ✔

c.i.

the forces between the ions do not affect the force on the spacecraft. ✔

there is no effect on the acceleration of the spacecraft. ✔

c.ii.

force per unit mass ✔

acting on a small/test/point mass «placed at the point in the field» ✔

d.i.

satellite has a much smaller mass/diameter/size than the planet «so approximates to a point mass» ✔

d.ii.

Examiners report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

d.i.

[N/A]

d.ii.

Syllabus sections

Core » Topic 2: Mechanics » 2.1 – Motion

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