Asimple pendulum of mass m swings at the end of a string of length ℓ. the highest point the pendulum reaches is a distance d vertically above its lowest point. in terms of these quantities, what is the kinetic energy of the pendulum when it reaches its lowest point?

Air is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. air enters the heat exchanger at 95 kpa and 20°c at a rate of 0.6 m^3/s. the combustion gases (cp = 1.10 kj/kg°c) enter at 160°c at a rate of 0.95 kg/s and leave at 95°c. determine the rate of heat transfer to the air and its outlet temperature.