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Power and Efficiency And a review of the work-energy theorem Whiteboards A bungee jumper jumps from a bridge. Explain the energy changes that occur during the jump, what work is being done, and what force(s) is/are doing the work as the jumper completes his jump A 1.5 kg block slides along a rough table and is brought to rest after travelling a distance of 2.4 m. The frictional force is assumed constant at 3.2 N. What work is done by friction? W F d (3.2 N )(2.4m) 7.7 J What is the coefficient of dynamic friction between the block and the table? 𝐹𝑓 = 𝜇 · 𝐹𝑁 3.2 = 𝜇 · (1.5)(9.81) 𝜇 = 0.22 What was the initial velocity of the block? W K 1 2 2 7.68 J (m)(v f vi ) 2 2 7.68 (0.5)(1.5)(0 vi ) vi 3.2 m s Power The rate at which work is performed In other words…the rate at which energy is transferred W E P t t Power Power can also be defined in terms of how quickly an object moves as a result of a force applied: W F d P F v t t Efficiency The power supplied to a motor is not always the same as the power that is actually used by the motor. The ratio of Power available to the Power used is a measure of the efficiency The larger the percentage of available power that is used, the greater the efficiency Pused % Eff x100 Pavailable Sample: The motor of an elevator develops power at a rate of 2500 W. At what constant speed can a 120 kg load be raised? P F v (mg ) v P 2500W v 2.12 m s mg (120kg)(9.81 m s 2 ) It was measured that the load was actually lifted at a speed of 1.5 m/s. What is the efficiency of the motor for this elevator? % Eff Pused 100 Pavailable % Eff (120)(9.81)(1.5) 100 70.6% 71% 2500