Hi All,

Once again, I awoke thinking of Trizebulax, where Spatz and Felicia live under a sky-green sky, subsisting on cat food and table scraps. I find it hard to shake off Trizebulax. What a strange and beautiful place. Somewhat like Earth.

It seems we need to complete yesterday's quiz. Henceforth we will refer to Trizebulax as T.

We want to know the speed of the Delrin hockey puck just before the next-to-final rebound. 

We  begin by formulating an expression for the kinetic energy just after the final rebound. The kinetic energy of the final rebound was dissipated as heat in sliding friction during the 1/2 foot slide to the final resting place of the puck.  By definition of the coefficient of friction, the drag force, D, during the final slide is equal to the coefficient of friction, F, multiplied by the weight, W,  of the puck on T. D = F x W. W equals the mass of the puck, m, times g, the gravitational acceleration on T. W = m x g. So the kinetic energy just after the final rebound = force times distance = F x W x .5 feet = .5 x m x g x .5 feet.

The coefficient of restitution, which was given as .5, is defined as the kinetic energy after the rebound, divided by the kinetic energy before the rebound. Because half the kinetic  energy was lost in the final rebound, the kinetic energy just before the final rebound is double the kinetic energy just after the final rebound. Therefore the kinetic energy just prior to the final rebound  = 2 x .5 x m x g x .5 feet = m x g x .5 feet.

The kinetic energy after the next-to-final rebound equals the kinetic energy prior to the final rebound plus the energy consumed by drag in the slide between the two walls. The slide distance between the two walls is double the distance of the final slide, consuming twice the energy consumed by the final slide. Therefore the energy consumed sliding between the walls = 2 x .5 x m x g x .5 feet = m x g x .5 feet. Thus the energy just after the next-to-final rebound is (m x g x .5 feet) + (m x g x .5 feet) = m x g x 1 foot.

We have seen that, with a coefficient of restitution of .5, the energy just before a rebound is double the energy just following a rebound. Therefore the kinetic energy just before the next-to-final rebound = 2 x m x g x 1 foot. Also, from Newton, we know that the kinetic energy is 1/2 x  m x V x V , where V is the speed of the puck. So we have 1/2 x m x V x V = 2 x m x g x 1 foot. This leaves us with V x V equal to 4 x g x 1 foot. The acceleration of gravity, g , on T,  was defined one half of the gravitational acceleration  on earth. Thus g = 1/2 x 32.2 feet per square second = 16.1 feet per square second. In conclusion, V x V = 4 x 16.1 feet per square second x 1 foot. Taking the square root we have V, the speed prior to the next-to-final rebound  = 8.03 feet per second. So you see, we actually did not need to know the weight of the puck to solve this problem.

I have no opinion on who will be president. These are strange times.

The sky of Trizebulax was given as green, not blue. The sky of Trizebulax is green because all other colors of the spectrum are reflected back into outer space.

The combined number of whiskers of Spatz and Felicia is 19.

A coefficient of restitution of 1.5 would violate conservation of energy, and might result in the next big bang.

I like the names Felicia and Spatz, but wonder if Spats should not have been named Spats for his white rear paws.

I hope there are no errors in my calculation of speed.

Have a great day.

Pete