The gure shows a pendulum of length l. = 3.0 m. Its bob (which effectively has all the mass} has speed v0 when the cord makes an angle 90 = 47 with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 8.4 m/s? What is the least value that v0 can have if the pendulum is to swingdown and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if 60 is increased by a few degrees? (a) Number \"1'? I Units m/s V (b) Number ".7? I Units m/s v (c) Number 11.26 Units m/s V Hint Assistance Used Did you conserve mechanical energy between the initial point and any given nal point? That is, did you set the sum of K and U at one point equal to the sum at another point? Key Ideas The mechanical energy Emec of a system is the sum of its kinetic energy K and potential energy U: Emec = K +U. . An isolated system is one in which no external force causes energy changes. If only conservative forces do work within an isolated system, then the mechanical energy Emec of the system cannot change. This principle of conservation of mechanical energy is written as K2 + U2 = K1 + U1, in which the subscripts refer to different instants during an energy transfer process. This conservation principle can also be written as AE mec = AK + AU = 0