A small ball of mass m is attached to a light string of length L and is swung in a vertical circle. At the top of the circle, the ball has speed v_{top} and the tension in the string is T_{top}. At the bottom of the circle, the ball has speed v_{bot} and the tension in the string is T_{bot}. Assume the string remains taut and the motion occurs in a region with constant gravitational acceleration g. Which of the following is a correct expression for the difference in tension, T_{bot} - T_{top}?