Morris S. answered • 07/12/19

Ph.D Chemist, Experienced Teacher

This is a good question and it's fun to think about. You start with a mass in steady circular motion: the force F is going to be mv^{2}/r. This is the force required to keep the mass circling at the same radius. Now suppose you double this force: the mass is going to curve more sharply, it will begin to move in a circle with radius r/2 tangent to the original circle with radius r. This new path brings the mass closer to the center of the circle. So now the motion of the mass and the force applied are no longer perpendicular. Some component of the force is now acting parallel to the motion of the mass: this will do work on the mass, and accelerate it to a higher speed.