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19 Vektorrechnung im 3-dimensionalen

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19.1 Multiplikation eines Vektors mit einem Skalar

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Beispiel 19 - 181
Eine Masse von m = 5 kg erfahre durch eine Kraft

 #
F eine Beschleunigung

a =( 2 1 4 ) m s 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqaaeaadaqaaqaaaOqaamaaFiaabaGaam yyaaGaay51GaGaeyypa0ZaaeWaaeaafaqabeWabaaabaGaaGOmaaqa aiabgkHiTiaaigdaaeaacaaI0aaaaaGaayjkaiaawMcaamaalaaaba GaamyBaaqaaiaadohadaahaaWcbeqaaiaaikdaaaaaaaaa@4124@

Bestimmen Sie den Vektor der Kraft #F . .

Mit    F =m a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqaaeaadaqaaqaaaOqaamaaFiaabaGaam OraaGaay51GaGaeyypa0JaamyBaiabgwSixpaaFiaabaGaamyyaaGa ay51Gaaaaa@3F42@  erhält man .

F =5 kg ( 2 1 4 ) m s 2 =( 10 5 20 )kg m s 2 =( 10 5 20 )N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabaGaaiaacaqaaeaadaqaaqaaaOqaamaaFiaabaGaam OraaGaay51GaGaeyypa0JaaGynaiaabccacaqGRbGaae4zaiaabcca cqGHflY1daqadaqaauaabeqadeaaaeaacaaIYaaabaGaeyOeI0IaaG ymaaqaaiaaisdaaaaacaGLOaGaayzkaaWaaSaaaeaacaWGTbaabaGa am4CamaaCaaaleqabaGaaGOmaaaaaaGccqGH9aqpdaqadaqaauaabe qadeaaaeaacaaIXaGaaGimaaqaaiabgkHiTiaaiwdaaeaacaaIYaGa aGimaaaaaiaawIcacaGLPaaacaWGRbGaam4zamaalaaabaGaamyBaa qaaiaadohadaahaaWcbeqaaiaaikdaaaaaaOGaeyypa0ZaaeWaaeaa faqabeWabaaabaGaaGymaiaaicdaaeaacqGHsislcaaI1aaabaGaaG OmaiaaicdaaaaacaGLOaGaayzkaaGaamOtaaaa@5B40@
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