A robotic floor polisher of mass \( M \) moves across a horizontal gym floor at a constant speed \( v \). The motor of the robot must provide a constant power \( P \) to overcome the kinetic friction between the polishing pads and the floor. A technician places an additional weight on the robot such that its total mass becomes \( 2M \). If the robot now moves at a constant speed of \( 2v \) across the same floor, what is the new power output required from the motor?