tasıt teknolojısı - carpısma testlerı_2016
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tasıt teknolojısı - carpısma testlerı_2016
MARMARA ÜNİVERSİTESİ TEKNOLOJİ FAKÜLTESİ TAŞIT TEKNOLOJİSİ ÇARPIŞMA TESTLERİ Abdullah DEMİR, Yrd. Doç. Dr. Ref. - Road Safety Strategy 2013 — 2020 Based on data for fatal/injury collisions provided by An Garda Síochána The most widely used vehicle safety systems worldwide are those modeled after the New Car Assessment Program (NCAP), introduced by the National Highway Traffic Safety Administration (NTHSA) in the U.S in 1979. This program has branched into several regional programs including Australia and New Zealand (ANCAP), Latin America (Latin NCAP), China (C-NCAP) and Europe (Euro NCAP). David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 Crash tests on cars in the European market are most often tested according to the Euro NCAP standards. These tests are not mandatory, so vehicles are either tested on initiative by Euro NCAP or by the manufacturers themselves [1]. The tests used are based on the Whole Vehicle Type Approval (ECWVTA) directive by the European Commission [7], which dictates the requirements for making a vehicle legal for sale within the European Union. Euro NCAP’s performance requirements are higher than those described in the directive, and are constantly increasing to inspire safety improvements. Safety ratings are reported by star ratings. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 NCAP Çarpışma Testi ve Derecelendirme Günümüzde güvenlik bir aracın satışında eskiye oranla daha önemlidir. Müşteriler için satış kararının en belirleyici unsurudur. Müşterilerin özel araç modellerinin performansına bağlı olarak güvenilir ve eksiksiz bir biçimde karşılaştırmalı bilgilere ulaşmaları önemlidir. Kanunen tüm yeni araç modelleri satılmadan önce belirli güvenlik testlerinden geçmelidir. Yine de yönetmelik yeni araçların güvenliği için asgari hukuki bir standart belirler, üreticileri bu asgari gereksinimlerin üzerine çıkma hususunda cesaretlendirme görevi Euro ve Ulusal Karayolu Trafik Emniyeti Kurumu (NHTSA) Yeni Araç Değerlendirme Programı'na (NCAP) aittir. Önemli Not: Test prosedürleri açısından Euro ve NHTSA arasında farklar olduğu unutulmamalıdır. Ön darbe testi: Ön darbe testi yönetmelik esasına göre Avrupa Geliştirilmiş Araç Güvenliği Kurulu tarafından geliştirilmiştir, fakat darbe hızı 8 km/h artırılmıştır. Ön darbe 64 km/h'de (40 mil/h) gerçekleştirilir, araç dengelenmiş deforme olabilen bariyere çarpar. Cansız mankenler üzerinden alınan değerler, ön koltuktaki yolcuların güvenliği belirlemek için kullanılır. Yan darbe testi: Darbe 50 km/h'de (30 mph) gerçekleşir. Yan darbe testi simülasyonu için aracın sürücü tarafına doğru ön kısmı deforme olabilen bir vagon çekilir. Sürücü güvenliğini belirlemek için manken üzerinden alınan değerler kullanılır. Kia, Hava Yastığı, 2010 NCAP Çarpışma Testi ve Derecelendirme Kia, Hava Yastığı, 2010 Çarpışma Testi Mankenleri Cansız mankenler üzerinde defalarca doğrudan çarpışma gerçekleştirilir. Mankenlerin görevi hayatidir: Kaza simülasyonları, bir kaza esnasında olası yaralanmaların tümünü göstermek için araç içindeki bir sürücü ve yolcu ile gerçekleştirilir. Mankenler normal sürücü ve yolcu değildir: Çelik gövdelidir, duyarlı bir ekipmanla donatılmıştır ve lastikle kaplıdır. Mankenler, çarpışma esnasında ne olduğu hakkında hayati bilgiler sağlar. Uzuvları tek tek açıklayan kılavuz, verinin nasıl sağlandığını açıklar. Baş: Mankenin başı alüminyumdan yapılmıştır ve içi lastikle doldurulmuştur. İçinde çarpışma esnasında beynin maruz kalabileceği kuvvetler ve hızlanma verilerini gösteren her biri dik açıyla yerleştirilmiş üç adet hız ölçer vardır. Boyun: Çarpma esnasında baş ileriye ve geriye doğru hareket ettiğinde, boyun üzerindeki bükülme, kopma ve eğilme kuvvetlerini tespit eden cihazlar vardır. Kollar: Kollarda herhangi bir alet bulunmaz. Çarpışma testinde kollar kontrolsüz olarak sallanır, ciddi yaralanmalar nadir görülmesine karşın kollar için tam bir koruma sağlamak zordur. Kia, Hava Yastığı, 2010 Çarpışma Testi Mankenleri Göğüs (ön darbe): Çelik kaburgaya ön darbe esnasında göğüs kafesinin esnemesini kaydeden bir cihaz takılmıştır. Örneğin emniyet kemerlerinden gelen gibi göğüs üzerindeki kuvvet büyük olduğunda yaralanma meydana gelir. Göğüs (yan darbe):Yan darbe mankeninin göğsü diğerlerinden farklıdır, göğüs basıncını ve bu basıncın hızını kaydetmek için üç kaburga ölçülür. Karın: Mankene, pelvis kemerine yerleştirilen göstergeler kullanılarak karında yaralanmaya neden olabilecek kuvvetleri kaydeden sensörler yerleştirilmiştir. Kırığa veya kalça çıkığına neden olabilen yanal kuvvetleri kaydeder. Üst Bacak: Bu bölüm pelvis, uyluk kemiği (uyluk) ve dizden oluşur. Uyluk kemiğindeki yük hücreleri; kırığın veya kalça çıkığının görülebileceği kalça eklemi dahil tüm bölümlerde yaralanmaya neden olabilecek önden çarpmalar hakkında veri saptar. Özellikle alt panele çarptığında mankenin dizlerinden iletilen kuvveti ölçmek için bir 'dizlik' kullanılır. Alt Bacak: Mankenlerin bacaklarının içerisine takılan göstergeler, kaval kemiğinin (incik kemiği) ve fibulanın (dizi ayak bileğine bağlar) yaralanma riskiyle birlikte bükme, kopartma ve eğilme kuvvetlerini de hesaplar. Ön darbe esnasında ayak ve dizlerin yaralanma riski, sürücünün ayak bölmesindeki esneme ve geriye doğru hareketi ölçüldükten sonra belirlenir. Çarpışma Testi Mankenleri Boyun, ön darbe mankeni Göğüs, yan darbe manken Kia, Hava Yastığı, 2010 The Euro NCAP tests have undergone several evaluations to estimate the effectiveness of the test procedures. These studies show that every added star represents a 12% reduction in collision fatality rates [9]. The crash tests conducted by Euro NCAP are [10]: • Frontal impact into a deformable offset barrier at 64 km/h. • Car to car side impact into the driver’s door at 50 km/h. • Pole side impact into rigid pole at 29 km/h. • Pedestrian impact at 40 km/h. • Rear impact whiplash injury test David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 These tests include child protection tests and the implementation of active safety assisting equipment like electronic stability control (ESC), seat belt reminders, speed limitation devices and anti-lock braking systems (ABS) [10]. Crash test scores are then declared with respect to and weighed according to: • 50% - Adult occupant assessment • 20% - Child occupant assessment • 20% - Pedestrian assessment • 10% - Safety assist assessment Figure 1: Euro NCAP’s weighing of test results from each assessment protocol to obtain the final score.C David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 Euro NCAP Point Distribution The Future of Active Safety Arthur D. Little 2014 Safety Assisting Equipment Unlike all other Euro NCAP testing procedures, the safety assist functions do not require any destructive testing. The aim with the protocol is promote standard fitment of safety assisting equipment such as Electronic Stability Control (ESC), Anti-Locking Brakes (ABS), Seat Belt Reminders and Speed Limitation Devices. The scoring of these systems is based on primarily the fitment of such equipment and secondary on the performance of this equipment. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 Frontal Impact Euro NCAP frontal impact tests are performed at an impact velocity of 64 km/h, 8 km/h higher than limits legislated by ECWVTA. The test shall represent two similar cars colliding with each other in a 40% offset impact, which is considered as the most common traffic accident resulting in severe injury or death. 40% meaning that the 40% of the vehicles frontal structure is struck in the impact. Figure A.2 Frontal impact crash test setup David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Frontal Impact The protection level is assessed using a frontal impact crash test dummy which measure accelerations, forces, deflections and deformations. Çarpışma testlerinde Pelvis: Leğen kemiği kullanılan mankenler Femur: Uyluk kemiği (Dummy) Tibia: Kaval kemiği Yapılan çarpışma testlerinde oluşabilecek yaralanmaları belirleyebilmek için elektronik sensörlerle donatılan son derece gelişmiş mankenler (dummy) kullanılmaktadır. Aynı zamanda üretici firmaların önerdiği çocuk koltukları da araca yerleştirilip çarpışmalarda çocukları koruyup korumadığı Crash test dummy results are presented using a five step scale. belirlenmektedir. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 Reading Text: In a frontal collision, kinetic energy is absorbed through deformation of the bumper, the front of the vehicle, and in severe cases the forward section of the passenger compartment (dash area). Axles, wheels (rims) and the engine limit the deformable length. Adequate deformation lengths and displaceable vehicle aggregates are necessary, however, in order to minimize passenger-compartment acceleration. Damage to the passenger compartment should be minimized. This concerns primarily • dash area (displacement of steering system, instrument panel, pedals, toe-panel intrusion), • underbody (lowering or tilting of seats), • the side structure (ability to open the doors after an accident). Acceleration measurements and evaluations of high-speed films enable deformation behavior to be analyzed precisely. Dummies of various sizes are used to simulate vehicle occupants and provide acceleration figures for head and chest as well as forces acting on thighs. Automotive Handbook Car to Car Side Impact Car side impact tests are performed by using a movable deformable barrier as seen in Figure. The impact is centered at the driver’s door at an impact velocity of 50 km/h. Figure : Car to car side impact test setup. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Car to Car Side Impact The aim with the test procedure is to assess any intrusion and occupant protection obtained from the cars side structure, but also to encourage the implementation of side airbags. To assess the occupant protection a side impact test dummy is used. Measures that are recorded are accelerations, forces, moments and deflections. Thoraks: Göğüs kafesi Rib: Kaburga kemiği Figure: Side impact crash test dummy rating. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Stockholm, 2011-01-28 Pole Side Impact The pole side impact tests goal is to encourage the fitting of head protection devices such as side impact head or curtain airbags and padding. Since the pole is relatively narrow, 10’’, or 254 mm, major intrusion is a common result. The test is performed by propelling the vehicle into a rigid pole at 29 km/h, representing the vehicle skidding into a pole or a tree, see Figure. Since 2009 this test is mandatory in the assessment process, and focuses on head, chest and abdomen protection. Before 2009 it was an optional test for manufacturers to demonstrate the efficiency of their head protection features. Figure: Pole side impact test setup David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Pole Side Impact Figure: Pole side impact crash test dummy rating. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Pedestrian Protection The pedestrian protection protocol has been a part of Euro NCAP since the start in 1997. Up to 2009 this test had a separate star rating but is now an integral part of the overall rating scheme seen in Figure A.1. Euro NCAP performs a series of tests to evaluate the pedestrian protection for both adult and child pedestrians. During the tests individual vehicle components are assessed to have a better control of the pedestrian impact locations. A legform is used to test the protection of the lower leg towards the front bumper, an upper legform to test the protection towards the leading edge of the bonnet and a child and adult headform to test the protection towards the bonnet top area and windscreen. The tests shall represent an impact velocity of 40 km/h. Figure: Pedestrian impact test setup and rating system. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Whiplash Protection The whiplash testing procedure is not a crash test involving the actual vehicle, but instead the seat and head rest assembly. The test is performed with the use of a crash sled on which the vehicle seat with a crash test dummy is fitted. The sled is then subjected to three different crash pulses with varying severity; low, medium and high. The low severity pulse accelerates the sled to approximately Dv=16 km/h in 100ms, and the high severity pulse to approximately Dv=25 km/h in 100ms [23][36]. These pulses are derived from both real world crashes and insurance industry research. The whole concept of whiplash injury is not yet entirely understood, especially the injury causing mechanisms of it, but the high frequency of this injury type has motivated Euro NCAP to include it into its adult occupant protection protocol since January 2009. Figure: Rear impact whiplash rating. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Child Protection The child occupant protection is a part of the frontal and car-to-car side impact testing procedures, but also addresses usability of the child restraints (CRS). Since it has shown that many child restraint users fail to secure the restraint safely to the car, Euro NCAP encourage improvements to child restraint design and the installation of standardized mountings such as ISOFIX. In the testing, dummies representing 18 month and 3 year old children are used (Figure 1-2), and the score depends on the child seats dynamic performance in frontal and side impact tests. Additionally, fitting instructions, airbag warning labels and the vehicles ability to accommodate the child restraint safely is also included in the overall scoring. Figure: Child protection testing rating scheme of 18 month old child. Figure: Child protection testing rating scheme of 3 year old child. David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Child Protection A- Dynamic Assessment B- Frontal Impact C- Side Impact David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, Child Protection D- Child Restraint Based Assessment E- Vehicle Based Assessment David Egertz, Sohrab Kazemahvazi, Stefan Hallström, “Novel Safety Requirements and Crash Test Standards for Light-Weight Urban Vehicles”, ÖZET…. Fig.: Some of the tests done by manufacturers to ensure that the occupants of their vehicles will be, so far as is practicable, safe in the event of an accident. At (a) is the simple basic zero offset frontal impact, at (b) is a 30 offset, at (c) a 40% offset and at (d) a pole impact test. A side impact test for representing an impact between two vehicles moving along lines at right angles to each other is shown at (e) while, at (f ), the vehicle that is struck is stationary. Finally, a rear end impact test is shown at (g). Automotive Engineering - Powertrain, Chassis System and Vehicle Body, Edited by David A. Crolla Presented by Ralph Hruschka MOMENTUM “Never design appearance only” Doğrusal momentum (“moment” ile karıştırılmamalıdır!), bir doğru boyunca hareket eden bir cismin hareket miktarının (taşıdığı hareketin) bir ölçüsüdür. Bir parçacığın doğrusal momentumu, eğer cismin hızı v ve kütlesi m ise, kütle ve hızın çarpımı olarak tanımlanır. Momentum p=mv şeklinde ifade edilir. Hız, v, vektörel olduğundan, p momentum da vektörel bir niceliktir (Bir vektörün skaler ile çarpımı hatırlanırsa, (skaler.vektör=vektör). Momentum vektörünün yönü hız ile aynı yönlüdür. Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 SI birim sisteminde birimi ise kg.m/s’dir. Nasıl ivme cismin hızındaki artışın, enerji de iş yapabilmenin bir ölçüsü ise, momentum da bir cismin sahip olduğu hareket miktarının ölçüsüdür. Momentum kavramını daha iyi anlamak için aynı hıza sahip olan bir kelebek ile bir kamyonu düşünelim. Bu iki cisim aynı hıza sahip olmalarına karşın, karşılarına çıkabilecek herhangi bir cisme verebilecekleri zarar oldukça farklıdır. Bu farkın nedeni, kütlelerinden dolayı taşıdıkları hareket miktarının farklı oluşundandır. Dolayısı ile sağduyusal olarak bunu bildiğimiz için her zaman hızı yavaş da olsa bir kamyonun üzerimize gelmesini istemeyiz ama kelebek için bunu fazlaca önemsemeyiz. Şimdi, taşınan hareket miktarı ile yani momentum ile kuvvet arasında nasıl bir ilişki olduğunu bulmaya çalışalım. Kuvvet ile momentum ilişkisinin; Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Şimdi, taşınan hareket miktarı ile yani momentum ile kuvvet arasında nasıl bir ilişki olduğunu bulmaya çalışalım. Kuvvet ile momentum ilişkisinin; şeklinde olduğunu görürüz. Bu, “bir parçacığın doğrusal momentumundaki değişme hızı, parçacığa etkiyen net kuvvete eşit” olduğunu ifade eder. Eğer bir parçacık üzerine etkiyen net kuvvet sıfır ise bu parçacığın momentumunun zamana göre türevi (değişimi) de sıfır olur ve dolayısı ile doğrusal momentum sabit kalır, yani korunur. Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Çarpışmalar Kütleleri m1 ve m2, hızları da sırası ile v1 ve v2 olan bir sistemi göz önüne alalım ve bu iki kütlenin çarpışması durumunda ilk ve son durumlarının ne olacağına bakalım. Eğer sisteme etki eden herhangi bir dış kuvvet (örneğin sürtünme) yok ise sistemin momentumu korunur. Buradan şu sonucu çıkarabiliriz: yalıtılmış bir sistemin çarpışmadan önceki (pi) toplam momentumu, çarpışmadan sonraki (ps) toplam momentuma eşittir. Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 İki aracın çarpışması: Trafik ışığında durmakta olan 1800 kg kütleli bir araca 900 kg kütleli küçük bir araç arkadan çarpar ve iki araç birlikte sürüklenir. Çarpışmadan önce küçük aracın hızı 20 m/s ise, çarpışmadan sonra birleşik kütlenin (araçların) sürüklenme hızı ne olur? Çözüm: Çarpışmadan önce sistemin momentumu: pi=m1.v1i +m2.v2i pi=(1800 kg).0+(900 kg).(20 m/s)=18000 kg.m/s Çarpışmadan sonraki sistemin momentumu: ps=(m1+m2).vs pi=ps (18000 kgm/s)=(m1+m2)vs vs=(18000 kgm/s)/(1800 kg+900 kg)=6,67 m/s Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Bir Boyutta Esnek ve Esnek Olmayan Çarpışmalar Dış kuvvetlerin olmadığı bir çarpışmada momentumun korunduğunu biliyoruz. Fakat çarpışmanın türüne bağlı olarak kinetik enerji sabit kalmayabilir. Kinetik enerjinin çarpışmadan önce ve sonra aynı olup olmaması çarpışmanın esnek veya esnek olmadığını belirlemede kullanılır. Esnek Çarpışma: Toplam momentum ve toplam kinetik enerjinin çarpışmadan önce ve sonra sabit kaldığı çarpışmadır. Esnek Olmayan Çarpışma: Momentumun korunduğu halde toplam kinetik enerjinin çarpışmadan önce ve sonra aynı olmadığı çarpışmadır. Tamamen Esnek Olmayan Çarpışmalar: Çarpışma sonrasında çarpışan kütlelerin birbirlerine yapışarak ortak bir v hızı ile hareket ettikleri çarpışmadır. Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Esnek Çarpışmalar Bölüm 9: Doğrusal Momentum, Hazırlayan: Dr. H.Sarı; http://eng.ankara.edu.tr/~hsari; Temmuz 2008 Example: Show mathematically why an 80,000 pound (36,000 kg) big rig traveling 2 mph (0.89 m/s) has the SAME MOMENTUM as a 4,000 pound (1,800 kg) sport utility vehicle traveling 40 mph (18 m/s). Momentum is the product of an object's mass and velocity. The formula is p = mv. The product of each is equivalent. The SI unit for momentum is the kilogram x meter/second (kg x m/s). Truck momentum = (36,000 kg)(0.89 m/s) = 32,000 kg x m/s SUV momentum= (1,800 kg)(18 m/s) = 32,000 kg x m/s Show mathematically why a small increase in your vehicle’s speed results in a tremendous increase in your vehicle’s kinetic energy. (For example: doubling your speed from 30 mph to 60 mph results in a quadrupling of your kinetic energy.) The velocity is squared in the equation; therefore if the speed is first doubled then squared, its kinetic energy must quadruple to keep the equation balanced. KE = 1/2 mv1^2 4KE = 1/2 m(2v1)^2 MOMENTUM Ref.: Dale Gary, Physics 111: Mechanics Lecture 12, NJIT Physics Department, March 16, 2016 How Good Are the Bumpers? In a crash test, a car of mass 1.5103 kg collides with a wall and rebounds as in figure. The initial and final velocities of the car are vi=-15 m/s and vf = 2.6 m/s, respectively. If the collision lasts for 0.15 s, find (a) the impulse delivered to the car due to the collision (b) the size and direction of the average force exerted on the car How Good Are the Bumpers? In a crash test, a car of mass 1.5103 kg collides with a wall and rebounds as in figure. The initial and final velocities of the car are vi=-15 m/s and vf = 2.6 m/s, respectively. If the collision lasts for 0.15 s, find (a) the impulse delivered to the car due to the collision (b) the size and direction of the average force exerted on the car pi mvi (1.5 103 kg)(15m / s) 2.25 104 kg m / s p f mv f (1.5 103 kg )(2.6m / s ) 0.39 104 kg m / s I p f pi mv f mvi (0.39 104 kg m / s) (2.25 104 kg m / s) 2.64 104 kg m / s p I 2.64 104 kg m / s Fav 1.76 105 N t t 0.15s Conservation of Momentum A 100 kg man and 50 kg woman on ice skates stand facing each other. If the woman pushes the man backwards so that his final speed is 1 m/s, at what speed does she recoil? (A) 0 (B) 0.5 m/s (C) 1 m/s (D) 1.414 m/s (E) 2 m/s Types of Collisions Momentum is conserved in any collision Inelastic collisions: rubber ball and hard ball Kinetic energy is not conserved Perfectly inelastic collisions occur when the objects stick together Elastic collisions: billiard ball both momentum and kinetic energy are conserved Actual collisions Most collisions fall between elastic and perfectly inelastic collisions Collisions Summary In an elastic collision, both momentum and kinetic energy are conserved In a non-perfect inelastic collision, momentum is conserved but kinetic energy is not. Moreover, the objects do not stick together In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same Elastic and perfectly inelastic collisions are limiting cases, most actual collisions fall in between these two types Momentum is conserved in all collisions More about Perfectly Inelastic Collisions When two objects stick together after the collision, they have undergone a perfectly inelastic collision Conservation of momentum m 1v1i m 2 v 2 i ( m 1 m 2 ) v f m 1 v1 i m 2 v 2 i vf m1 m 2 Kinetic energy is NOT conserved An SUV Versus a Compact An SUV with mass 1.80103 kg is travelling eastbound at +15.0 m/s, while a compact car with mass 9.00102 kg is travelling westbound at -15.0 m/s. The cars collide head-on, becoming entangled. Find the speed of the entangled cars after the collision. Find the change in the velocity of each car. Find the change in the kinetic energy of the system consisting of both cars. An SUV Versus a Compact Find the speed of the entangled cars m 1.80 103 kg, v 15m / s 1 1i after the collision. 2 m2 9.00 10 kg, v2i 15m / s pi p f m1v1i m2v2i (m1 m2 )v f m1v1i m2 v2i vf m1 m2 v f 5.00m / s An SUV Versus a Compact Find the change in the velocity of each car. m1 1.80 103 kg, v1i 15m / s v f 5.00m / s m2 9.00 102 kg, v2i 15m / s v1 v f v1i 10.0m / s v2 v f v2i 20.0m / s m1v1 m1 (v f v1i ) 1.8 104 kg m / s m2 v2 m2 (v f v2i ) 1.8 104 kg m / s m1v1 m2 v2 0 An SUV Versus a Compact Find the change in the kinetic energy 3 m 1 . 80 10 kg, v1i 15m / s of the system consisting of both cars. 1 m2 9.00 102 kg, v2i 15m / s v f 5.00m / s 1 1 2 KEi m1v1i m2v22i 3.04 105 J 2 2 1 1 2 KE f m1v1 f m2 v22 f 3.38 104 J 2 2 KE KE f KEi 2.70 105 J More About Elastic Collisions Both momentum and kinetic energy are conserved m1v1i m 2 v 2 i m1v1 f m 2 v 2 f 1 1 1 1 2 2 2 m1v1i m 2 v 2 i m1v1 f m 2 v 22 f 2 2 2 2 Typically have two unknowns Momentum is a vector quantity Direction is important Be sure to have the correct signs Solve the equations simultaneously Elastic Collisions A simpler equation can be used in place of the KE equation 1 1 1 1 2 2 2 m 1 v 1 i m 2 v 2 i m 1 v 1 f m 2 v 22 f 2 2 2 2 m 1 ( v 12i v 12 f ) m 2 ( v 22 f v 22 i ) v v (v v ) m 1 ( v 11i i v 1 f ) ( v21 ii v 1 f ) m 21(fv 2 f v 2 2i ) f( v 2 f v 2 i ) m 1v1i m 2 v 2 i m 1v1 f m 2 v 2 f m 1 ( v1i v1 f ) m 2 ( v 2 f v 2 i ) v1i v1 f v 2 f v 2 i m 1v1i m 2 v 2 i m 1v1 f m 2 v 2 f Summary of Types of Collisions In an elastic collision, both momentum and kinetic energy are conserved v1i v1 f v 2 f v 2 i m 1v1i m 2 v 2 i m 1v1 f m 2 v 2 f In an inelastic collision, momentum is conserved but kinetic energy is not In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same Conservation of Momentum An object of mass m moves to the right with a speed v. It collides head-on with an object of mass 3m moving with speed v/3 in the opposite direction. If the two objects stick together, what is the speed of the combined object, of mass 4m, after the collision? (A) (B) (C) (D) (E) 0 v/2 v 2v 4v Problem Solving for 1D Collisions, 1 Coordinates: Set up a coordinate axis and define the velocities with respect to this axis It is convenient to make your axis coincide with one of the initial velocities Diagram: In your sketch, draw all the velocity vectors and label the velocities and the masses Problem Solving for 1D Collisions, 2 Conservation of Momentum: Write a general expression for the total momentum of the system before and after the collision Equate the two total momentum expressions Fill in the known values m 1v1i m 2 v 2 i m 1v1 f m 2 v 2 f Problem Solving for 1D Collisions, 3 Conservation of Energy: If the collision is elastic, write a second equation for conservation of KE, or the alternative equation This only applies to perfectly elastic collisions v1i v1 f v 2 f v 2 i Solve: the resulting equations simultaneously One-Dimension vs Two-Dimension Two-Dimensional Collisions For a general collision of two objects in two-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved m 1 v1ix m 2 v 2 ix m 1 v1 fx m 2 v 2 fx m 1 v1iy m 2 v 2 iy m 1 v1 fy m 2 v 2 fy Two-Dimensional Collisions The momentum is conserved in all directions m 1 v1ix m 2 v 2 ix m 1 v1 fx m 2 v 2 fx Use subscripts for Identifying the object m 1 v1iy m 2 v 2 iy m 1 v1 fy m 2 v 2 fy Indicating initial or final values The velocity components If the collision is elastic, use conservation of kinetic energy as a second equation Remember, the simpler equation can only be used for one-dimensional situations v1i v1 f v 2 f v 2 i Glancing Collisions The “after” velocities have x and y components Momentum is conserved in the x direction and in the y direction Apply conservation of momentum separately to each direction mv m v mv m v 1 1 ix 2 2 ix 1 1 fx 2 2 fx m 1 v1iy m 2 v 2 iy m 1 v1 fy m 2 v 2 fy 2-D Collision, example Particle 1 is moving at velocity v1i and particle 2 is at rest In the x-direction, the initial momentum is m1v1i In the y-direction, the initial momentum is 0 2-D Collision, example cont. After the collision, the momentum in the x-direction is m1v1f cos q + m2v2f cos f After the collision, the momentum in the y-direction is m1v1f sin q + m2v2f sin f m 1 v1i 0 m 1 v1 f cos m 2 v 2 f cos 0 0 m 1 v1 f sin m 2 v 2 f sin If the collision is elastic, apply the kinetic energy equation 1 1 1 m 1 v 12i m 1 v 12 f m 2 v 22 f 2 2 2 Collision at an Intersection A car with mass 1.5×103 kg traveling east at a speed of 25 m/s collides at an intersection with a 2.5×103 kg van traveling north at a speed of 20 m/s. Find the magnitude and direction of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected. mc 1.5 103 kg, mv 2.5 103 kg vcix 25m / s, vviy 20m / s, v f ? ? Collision at an Intersection mc 1.5 103 kg , mv 2.5 103 kg vcix 25 m/s, vviy 20 m/s, v f ? ? p p xi mc vcix mv vvix mc vcix 3.75 104 kg m/s xf mc vcfx mv vvfx (mc mv )v f cos 3.75 104 kg m/s (4.00 103 kg )v f cos p p yi mc vciy mv vviy mv vviy 5.00 104 kg m/s yf mc vcfy mv vvfy (mc mv )v f sin 5.00 104 kg m/s (4.00 103 kg )v f sin Collision at an Intersection mc 1.5 103 kg, mv 2.5 103 kg vcix 25m / s, vviy 20m / s, v f ? ? 5.00 104 kg m/s (4.00 103 kg )v f sin 3.75 104 kg m/s (4.00 103 kg )v f cos 5.00 104 kg m / s tan 1.33 4 3.75 10 kg m / s tan 1 (1.33) 53.1 5.00 104 kg m/s vf 15.6 m/s 3 (4.00 10 kg ) sin 53.1 The Center of Mass How should we define the position of the moving body ? What is y for Ug = mgy ? Take the average position of mass. Call “Center of Mass” (COM or CM) The Center of Mass There is a special point in a system or object, called the center of mass, that moves as if all of the mass of the system is concentrated at that point The CM of an object or a system is the point, where the object or the system can be balanced in the uniform gravitational field The Center of Mass The center of mass of any symmetric object lies on an axis of symmetry and on any plane of symmetry If the object has uniform density The CM may reside inside the body, or outside the body Where is the Center of Mass ? The center of mass of particles Two bodies in 1 dimension xCM m1 x1 m2 x2 m1 m2