Dynamics - Work, energy and power — Power

About this lesson

This unit introduces the concept of power as the time rate of doing work, distinguishing it from work itself. It defines power mathematically as the derivative of work with respect to time, and also presents the average power over a time interval. The unit explains that when force and velocity are in the same direction, power equals force times velocity, and that power is a scalar quantity. It covers the relationship between power, work, and time, including using integration to find total work from a variable power function. The unit also discusses variable and maximum power, noting that for constant force, power varies directly with velocity, and maximum power occurs at maximum velocity. It lists several units of power: watt (Newton·m/s), kg.wt·m/sec, erg/sec, and horse (defined as 75 kg.wt·m/sec), with conversion rules between them (1 kg.wt·m/sec = 9.8 watts, 1 watt = 10^7 erg/sec, 1 kilowatt = 1000 watts, 1 horse = 735 watts = 0.735 kilowatt). The unit provides worked examples and exercises involving calculating power for various scenarios: a person ascending stairs, a plane engine, a car moving on horizontal and inclined roads against resistances, a train ascending and descending slopes, a worker loading boxes, and particles moving under forces with given displacement vectors. Students learn to compute power from force and velocity, to find work done using integration when power is a function of time, and to apply the work-energy principle to find time or velocity changes. The exercises also include problems on maximum velocity, resistance forces, and power of engines in different contexts, including variable power functions and vector calculus for force and displacement. By the end, students should be able to define power, convert between units, calculate average and instantaneous power, and solve problems involving constant and variable power in mechanical systems.