An electric motor consumes an input power of 10 kW and operates with an efficiency of 80 % . It is used to pull a block of mass 400 kg horizontally across a rough surface at a constant speed. If the coefficient of kinetic friction between the block and the surface is 0.5 , what is the speed of the block? (Take g = 10 m s ⁻² )

Step-by-step solution

The useful mechanical power output of the motor is a fraction of the input electrical power, determined by its efficiency. P_ out = P_ in P_ out = 80 100 10000 W = 8000 W The frictional force acting on the block on a horizontal surface is given by f = _k mg . f = 0.5 400 10 = 2000 N Since the block moves at a constant speed, the pulling force F exerted by the motor must exactly balance the frictional force. F = f = 2000 N Using the relation between power, force, and velocity ( P = F v ): 8000 = 2000 v v = 8000 2000