Question 18N.2.SL.TZ0.1
| Date | November 2018 | Marks available | [Maximum mark: 12] | Reference code | 18N.2.SL.TZ0.1 |
| Level | SL | Paper | 2 | Time zone | TZ0 |
| Command term | Determine, Estimate, Explain, Outline, Suggest | Question number | 1 | Adapted from | N/A |
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 × 10–6 kg 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.
Determine the initial acceleration of the spacecraft.
[2]
change in momentum each second = 6.6 × 10−6 × 5.2 × 104 «= 3.4 × 10−1 kg m s−1» ✔
acceleration = « =» 4.6 × 10−4 «m s−2» ✔
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.
Estimate the maximum speed of the spacecraft.
[2]
ALTERNATIVE 1:
(considering the acceleration of the spacecraft)
time for acceleration = = «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» ✔
Outline why scientists sometimes use estimates in making calculations.
[1]
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 ✔
In practice, the ions leave the spacecraft at a range of angles as shown.
Outline why the ions are likely to spread out.
[2]
ions have same (sign of) charge ✔
ions repel each other ✔
Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.
[2]
the forces between the ions do not affect the force on the spacecraft. ✔
there is no effect on the acceleration of the spacecraft. ✔
On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.
Outline what is meant by the gravitational field strength at a point.
[2]
force per unit mass ✔
acting on a small/test/point mass «placed at the point in the field» ✔
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]
satellite has a much smaller mass/diameter/size than the planet «so approximates to a point mass» ✔