A Classical Approach of Newtonian Mechanics

6 CONSERVATION OF MOMENTUM 6.2 Two-component systems m 1 m 2 f F 1 F^2 12 f 21 x 1 x 2 x^ Here, ̇ is a convenient shorthand for ...

6 CONSERVATION OF MOMENTUM 6.2 Two-component systems This is particularly the case if the internal forces, f 12 and f 21 , are c ...

6 CONSERVATION OF MOMENTUM 6.2 Two-component systems balloon gondola x xg^ sandbag cable xw Figure 46: An example two-component ...

6 CONSERVATION OF MOMENTUM 6.2 Two-component systems vr vb cannon cannonball ground Figure 47: Another example two-component sys ...

6 CONSERVATION OF MOMENTUM 6.3 Multi-component systems velocity vr of the cannon? Let us first identify all of the forces acting ...

6 CONSERVATION OF MOMENTUM 6.3 Multi-component systems X X X fj i Figure 48: A 3 - dimensional dynamical system consisting of ma ...

6 CONSERVATION OF MOMENTUM 6.3 Multi-component systems i=1 i=1 . . X i=1. (6.20) i=1 , (6.21) N i=1 mi^ N i=1 mi^ where M = .N m ...

6 CONSERVATION OF MOMENTUM 6.4 Rocket science trajectory of centre of mass Figure 49: The unfortunate history of the planet Kryp ...

6 CONSERVATION OF MOMENTUM 6.4 Rocket science rocket propellant Figure 50: A rocket. t t+dt v (^) M+m M+m+dm v+dv dm v-u^ Figu ...

6 CONSERVATION OF MOMENTUM 6.4 Rocket science ! ∫ M f p assumed to be in outer space. It follows that the total momentum of the ...

6 CONSERVATION OF MOMENTUM 6.5 Impulses Let us now consider the factors which might influence the design of a rocket for use in ...

6 CONSERVATION OF MOMENTUM 6.5 Impulses ui uf wall after m before +ve Figure 52: A ball bouncing off a wall. t 1 t 2 t Figure 53 ...

6 CONSERVATION OF MOMENTUM 6.5 Impulses ∫ f Figure 53 shows the typical time history of an impulsive force, f(t). It can be seen ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension (^) before after Figure 54: A collision in 1 - dimension. The net cha ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension momentum of the system is a conserved quantity. Equating the total mo ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension the colliding objects. In a totally inelastic collision, the two obje ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension is trivially satisfied, because both the left- and right-hand sides a ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension the cue ball with great force in such a manner that it slides, rather ...

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension y vf2 m 2 m 1 vi1  2 m 2  1 m 1 i1 x vf1 Figure 55: A collision in ...

6 CONSERVATION OF MOMENTUM 6.7 Collisions in 2 - dimensions 6.7 Collisions in 2 - dimensions Suppose that an object of mass m 1 ...