A Classical Approach of Newtonian Mechanics

5 CONSERVATION OF ENERGY 5.4 Conservative and non-conservative force-fields X X Wi = A fi(r)·dr (5.22) W = A f(r)·dr. (5.25) net ...

5 CONSERVATION OF ENERGY 5.4 Conservative and non-conservative force-fields ∫ B A Figure 40: Two alternative paths between point ...

5 CONSERVATION OF ENERGY 5.4 Conservative and non-conservative force-fields ·d ·d value of that integral picks up a minus sign: ...

5 CONSERVATION OF ENERGY 5.4 Conservative and non-conservative force-fields · ∝ i i (^) Figure 41: Closed circuit over a rough h ...

5 CONSERVATION OF ENERGY 5.5 Potential energy · ∆K = O f·dr. (5.34) 5.5 Potential energy Consider a body moving in a conservativ ...

5 CONSERVATION OF ENERGY 5.6 Hooke’s law i.e., the sum of the kinetic energy and the function U remains constant as the body mov ...

5 CONSERVATION OF ENERGY 5.6 Hooke’s law 2 k xB − 2 k xA 2 k xB − 2 k xA. (5.39) Figure 42: Mass on a spring the mass is directl ...

5 CONSERVATION OF ENERGY 5.6 Hooke’s law U(x) = − f(x ) dx. (5.41) → 0 Hence, the potential energy of the mass takes the form U( ...

5 CONSERVATION OF ENERGY 5.7 Motion in a general 1 - dimensional potential k 0 The total energy of the mass shown in Fig. 42 is ...

5 CONSERVATION OF ENERGY 5.7 Motion in a general 1 - dimensional potential E 2 x - > E 1 E 0 0 x 0 x 1 x 2 Figure 43: General ...

5 CONSERVATION OF ENERGY 5.7 Motion in a general 1 - dimensional potential In other words, a equilibrium state corresponds to ei ...

5 CONSERVATION OF ENERGY 5.8 Power Stable Equilibrium Unstable Equilibrium Neutral Equilibrium x - > Figure 44: Different typ ...

5 CONSERVATION OF ENERGY 5.8 Power where v = dr/dt is the object’s instantaneous velocity. Note that power can be positive or ne ...

5 CONSERVATION OF ENERGY 5.8 Power R F  f chest dock m g Worked example 5.2: Dragging a treasure chest Question: A pirate drag ...

5 CONSERVATION OF ENERGY 5.8 Power m 50 The work WJ done by the frictional force is WJ = −f x = −69.89 × 6 = −419.3 J. Note that ...

5 CONSERVATION OF ENERGY 5.8 Power A The work WJ done by the external force in extending the spring from 0 to x is Hence, WJ = x ...

5 CONSERVATION OF ENERGY 5.8 Power B ., By energy conservation, ∆K = −∆U, where K represents kinetic energy. How- ever, since th ...

5 CONSERVATION OF ENERGY 5.8 Power where x = h/ sin θ is the distance the block slides. The minus sign indicates that f acts in ...

5 CONSERVATION OF ENERGY 5.8 Power 160 × 10 3 × where the left-hand side is the power output of the engine, and the right-hand s ...

6 CONSERVATION OF MOMENTUM 6 Conservation of momentum 6.1 Introduction Up to now, we have only analyzed the behaviour of dynamic ...