Chapter 1 - Assets - Cambridge University Press

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Cambridge University Press978-0-521-73830-9 - Physics 2 for OCRGurinder Chadha and David SangExcerptMore informationChapter 1: Momentumconserved. We have to consider objects which forma closed system – that is, no external force acts onthem. The principle of conservation of momentumstates that:Within a closed system, the total momentum inThe principle of conservation of momentum can alsobe expressed as follows:total momentum of objects before collision= total momentum of objects after collisionA group of colliding objects always has as muchmomentum after the collision as it had beforethe collision. This principle is illustrated inWorked example 1.Worked example 1In Figure 1.5, trolley A of mass 0.80 kg travellingat a velocity of 3.0 m s collides head-on witha stationary trolley B. Trolley B has twice themass of trolley A. The trolleys stick together andhave a common velocity of 1.0 m s after thecollision. Show that momentum is conserved inthis collision.beforepositivedirectionafteru A = 3.0 m s –1 u B = 0 v A+B = 1.0 m s –1A 0.80 kg B A 0.80 kg B0.80 kg 0.80 kg 0.80 kg 0.80 kgStep 1 Make a sketch using the information givenin the question. Notice that we need two diagramsto show the situations before and after the collision.Similarly, we need two calculations – one for themomentum of the trolleys before the collision andone for their momentum after the collision.Step 2 Calculate the momentum before thecollision:momentum of trolleys before collision= m A u A + m B u B= (0.80 3.0) + 0= 2.4 kg m s The trolley B has no momentum before thecollision, because it is not moving.Step 3 Calculate the momentum after the collision:momentum of trolleys after collision= (m A + m B ) v A+B= (0.80 + 1.60) 1.0= 2.4 kg m s So, both before and after the collision, the trolleyshave a combined momentum of 2.4 kg m s –1 .Momentum has been conserved.SAQ2 Calculate the momentum of each of the followingobjects:a A 0.50 kg stone travelling at a velocity of 20 m s .b A 25-tonne bus travelling at20 m s Hinton a road.c An electron travelling at 2.0 10 7 m s .The mass of the electron is9.1 10 Answerkg.4Figure 1.5 The state of the trolleys A and B,before and after the collision.continued3Two balls, each of mass 0.50 kg,Hintcollide as shown in Figure 1.6.Show that their total momentum beforethe collision is equal to their totalAnswermomentum after the collision.© Cambridge University Press www.cambridge.org
Cambridge University Press978-0-521-73830-9 - Physics 2 for OCRGurinder Chadha and David SangExcerptMore informationChapter 1: Momentumbeforeafter2.0 m s –1 2.0 m s –1 1.0 m s –1A B A BFigure 1.6 For SAQ 3.Motor manufacturers make use of test labs toinvestigate how their cars respond to impacts. Whena car is designed, the manufacturers combine soft,compressible materials that absorb energy withrigid structures that protect the car’s occupants.Old-fashioned cars had much more rigid structures.In a collision, they were more likely to bounce backand the violent forces involved were much morelikely to prove fatal.3.0 m s –1 v v v vUnderstanding collisionsThe cars in Figure 1.7 have been badly damaged by acollision. The front of a car is designed to absorb theimpact of the crash. It has a ‘crumple zone’, whichcollapses on impact. This absorbs most of the kineticenergy that the car had before the collision. It is betterthat the car’s kinetic energy should be transferred tothe crumple zone than to the driver and passengers.Two types of collisionWhen two objects collide, they may crumple anddeform. Their kinetic energy may also disappearcompletely and they come to a halt. This is anexample of an inelastic collision. Alternatively, theymay spring apart, retaining all of their kinetic energy.This is a perfectly elastic collision. In practice, inmost collisions, some kinetic energy is transformedinto other forms (e.g. heat or sound) and the collisionis inelastic. Previously we described the collisions asbeing ‘springy’ or ‘sticky’. We should now use theperfectly elastic and inelastic.We will look at examples of these two typesof collision and consider what happens to linearmomentum and kinetic energy in each.A perfectly elastic collisionTwo identical objects A and B, moving at the samespeed but in opposite directions, have a head-oncollision, as shown in Figure 1.8. This is a perfectlyelastic collision. Each object bounces back with itsvelocity reversed.beforepositivedirectionafterA B A BmmmmFigure 1.7 The front of each car has crumpled in, asa result of a head-on collision.Figure 1.8 Two objects may collide in differentways: this is an elastic collision. An inelastic collisionof the same two objects is shown in Figure 1.9.5© Cambridge University Press www.cambridge.org
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Chapter 1 - Assets - Cambridge University Press

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