TAP 222-4: Momentum questions

Transcription

1 TAP -4: Moentu questions These questions change in difficulty and ask you to relate ipulse to change of oentu. 1. Thrust SSC is a supersonic car powered by jet engines giving a total thrust of 180 kn. Calculate the ipulse applied to the car when the engines run for 4 seconds. Assue the thrust is the only force acting on the car, which has a ass of kg. Calculate the increase in speed of the car after the 4 s.. One suggestion for powering spacecraft engines of the future is an ion engine. A bea of ions (charged atos) is fired backwards, propelling the spacecraft forwards. In one test, xenon ions were used. Consider how using xenon ions would copare with using krypton ions, which are lighter. If equal nubers of each ion were propelled back per second, at the sae speed, which type of ion would you expect to give ore thrust? Explain your answer The ass of a xenon ion is kg, and it can be ejected at a speed of s. Calculate the nuber of ions that would have to be eitted per second to generate a thrust of 0.1 N (a typical value of the thrust fro such an engine). 3. When holding a hose fire-fighters need to ensure that they are not pushed backwards, especially if the water is ejected at a high speed. Explain why fire-fighters experience a backwards force. 0 kg of water is ejected horizontally in 10 s; the speed of the water leaving the nozzle is 30 s. Calculate the force experienced by a fire-fighter holding the hose.

2 4. A spacecraft is approaching the planet Zog and needs to slow down. To do so it fires a jet of forwards. Explain how firing forwards slows the rocket down. The rocket has a ass of kg. The can be fired forward at a speed of s relative to the rocket. Calculate the ass of ust the rocket eject to reduce its speed by 5 s. Ignore the change in the rocket s ass due to the ejection of. 5. Air of density 1.3 kg 3 strikes a sail of area 15. The air is initially oving at 5 s, assue it is brought to rest when it hits the sail. Calculate the ass of air is brought to rest in each second? Hence calculate the average force the air exerts on the sail. 6. A kestrel is a bird of prey which searches for prey by hovering above grassy areas. Using your ideas about oentu, suggest how a kestrel is able to hover. The kestrel has a ass of 00 g and it pushes down a colun of air of area 600 c. Estiate the downward speed given to the air by the kestrel g to be 9.8 N kg, density of air 1.3 kg 3.

3 Estiate the iniu power the kestrel needs to hover? Suggest why there are no large birds which can hover? (Soe large birds, such as buzzards and condors, ay appear to hover, but are not really doing so. They use upwards currents of air therals to stay up.) 7. 5 kg s -1 of air at 10 s -1 is taken in by a jet engine that burns 1 kg fuel each second. The exhaust ses are ejected at 50 s -1 relative to the engine. a) Calculate the velocity change of the air. b) Calculate the oentu change per second of the air and also of the fuel. c) What is the thrust of the jet engine? 8. The H-3 Sea King Helicopter has a ass of about 5400 kg (including crew). It is hovering over the sea on a rescue ission. The rotors have a radius of about 10. Air density is 1. kg -3. Assue g 10 N kg -1 a) What lift force is needed to keep the helicopter hovering? b) What downward velocity is given to the air by the hovering helicopter? 9. In June 1999, the ESA space probe Giotto ade an Earth fly-by following issions to investigate Halley s Coet in 1986 and Coet Grigg-Skjellerup in 199. A ajor hazard to Giotto was the large nuber of high-speed solid particles ( dust ) that ake up coets tails. At collision speeds likely to occur, a 0.1 g particle can penetrate an aluiniu plate 8 c thick. To protect the probe s instruents, engineers designed a dust shield of two protective sheets 3 c apart. The front shield is a sheet of aluiniu 1 thick which retards and vaporises all but the largest particles. The rear shield is a 1 thick sheet of Kevlar (as used in bullet-proof vests) which traps any reaining debris and becoes heated as a result. The Giotto probe has a ass of 960 kg. Suppose it is travelling at.0 k s -1 when it encounters a dust particle of ass 0.10 g travelling at 50 k s -1 in the opposite direction to the probe. The particle is trapped in the shield.

4 a) Show that the collision has a negligible effect on Giotto s velocity. b) If the collision takes 1.0 s, calculate the average force exerted on the probe. c) Explain whether this is an elastic or an inelastic collision.

5 Practical Advice These questions practise the analysis of oentu and ipulse applied to jets and rockets. To ake a valid attept at all of the requires a high degree of failiarity with the basic terinology and equations. Apart fro the first question they are definitely not for war-up. The second question is based on a real technology. Question 5 is quite tough. Further inforation about the liits on the size of birds can be found in Barrow and Tipler, The Cosological Anthropic Principle (Oxford: Oxford University Press) p A collision question concerning the Giotto probe is also included Answers and Worked Solutions 1. Thrust Ft N s Ft v u N s Δv Δv 7 s. Xenon ions would provide ore thrust. This is because there would be a greater oentu change per second since they have a greater ass than krypton ions. Let ass of each ion, n nuber of ions eitted per second, v speed of ejection of ions. Then, ipulse, F Δ t change in oentu ( n) (v 0): so F.1 N 1 s 19 n s v 5 4 (. 10 kg) ( s ) 0 3. The pup pushes the water forwards, which by Newton s third law exerts a force of equal size back on the hose and the pup syste. The hose, gripped by the firefighter, exerts a backward force on the fire-fighter.. F t v t 0 kg 30 s 1 60 N. 10 s 4. To eject the, the rocket exerts a forward force on the. By Newton s third law, the exerts a force of equal size back on the rocket. This force is responsible for the deceleration of the rocket. Δv rocket rocket Δv rocket kg 5 s s 50 kg. 5. Δ ass of air brought to rest per second, v initial speed of air, A area of sail, ρ density of air:

6 Δ v ρ ρav 1.3 kg t t Δ F v 98 kg s t t s 5 s kg s N. 6. The kestrel pushes down on the air, giving it downward oentu. The air pushes back up on the kestrel s wing (by Newton s third law). If this upward push equals the weight of the kestrel, the bird can hover at a constant vertical velocity of 0 s. v downward speed gained by air, ρ density of air, A area of air colun pushed down, b ass of bird: For the bird to hover, the push of the air ust equal b g, the weight of the bird. vδ downward force on air F Δ but ρav so F ρav downward force on air upward force on kestrel ρav bg bg v ρa v 1.3 kg v 5.0 s iniu power Fv 0. kg kg 9.8 N kg -3 ( N kg s ) 9.8 W 7. a) Velocity change of the air (50-10) 400 s -1 b) Moentu change per second of the air 5 x ,000 kg s - Moentu change per second of the fuel 1 x kg s - Δv c) Engine thrust F total oentu change/second 10, ,50 N 8. a) Force is needed to keep the helicopter hovering weight 5400 x N

7 b) vδ downward forceon air F Δ but ρav so F ρav downwardforceon air weight of helicopter ρav g v b b g ρa v 1. kg v 1 s ( Πx10x10) 9. a) Initial oentu, p 960 kg x.0 x 10 3 s -1 (1.0 x 10-4 kg x 50 x 10 3 s -1 ) 1.90 x 10 6 kg s -1 (5.0 kg s -1 so about 1.90 x 10 6 kg s -1 ) Final ass, 960 kg x 10-4 kg so about 960 kg Final velocity, v p/ Since p and are extreely close to Giotto s initial ass and velocity, Giotto s final velocity ust be extreely close to its initial velocity. b) Dust: Δv 50 - (-) 5 k s -1 Δv F (1.0 x 10-4 x 5 / 1 x N c) Collision is inelastic. Trapping dust results in heating of the shield, so there ust be a loss of kinetic energy fro the dust. ) External References Questions 1-6: are taken fro Advancing Physics Chapter 11, 180S Question 9: This is taken fro Salters Horners Advanced Physics, Section TRA, Additional sheets 8 and 9