1. 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 ms–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.
(a) Determine the initial acceleration of the spacecraft.
(b) 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.
(i) Estimate the maximum speed of the spacecraft.
(ii) Outline why scientists sometimes use estimates in making calculations.
(c) In practice, the ions leave the spacecraft at a range of angles as shown.
(i) Outline why the ions are likely to spread out.
(ii) Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.
(d) On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.
(i) Outline what is meant by the gravitational field strength at a point.
(ii) 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.
2. A lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.
The following data are available for the lamps when at their working temperature.
(a) Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.
(b) Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.
(c) One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline one other electrical advantage of this system compared to one in which the lamps are connected in series.
3. A chicken’s egg of mass 58 g is dropped onto grass from a height of 1.1 m. The egg comes to rest in a time of 55 ms. Assume that air resistance is negligible and that the egg does not bounce or break.
(a) Determine the magnitude of the average decelerating force that the ground exerts on the egg.
(b) Explain why the egg is likely to break when dropped onto concrete from the same height.