William Gravesande in 1722 published an experiment in which brass balls were dropped from varying heights onto a soft clay surface. He found that a ball with twice the speed of another would leave an indentation four times as deep.
Some years later, Emilie du Chatelet republished the experiment and proposed that each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity and the deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy.
So is kinetic energy inversely (squared) proportional to the quantity of clay displaced or is it proportional to the depth to which the ball will go ? Please provide an explanation not based on experimental data as most of 19th century physicists do. Also are any one of the effects mentioned above due to momentum of the ball ?
i am not asking about diameter and kinetic energy relationships , i am just askin about a derivation for the depth and displaced amount of material relationship with kinetic energy of some object.
