Clickety-clack

One single ball at the end of a Newton's cradle is pulled back by a very small angle and released. Every time the ball hits the four other hanging balls, a single ball lifts off the other side with 0.99 of the energy of the incoming ball (as in the first 10 seconds of this video). Each impact also makes a click. If \(T\) is the time it takes between the first and second clicks, and \(T_{25}\) is the time it takes between the 25th and 26th clicks, what is \(T/T_{25}\)?

Details and assumptions

• The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
• Make the approximation that the bottom balls remain stationary and that no time passes between the impact of one ball and the lift off of the opposite side ball.