Yup, energy is conserved in isolated systems. Thanks for the insight. Would you believe that i finished Mechanics A-level at school(Average mark 87.5%) and i was not familiar with the reason of equating Loss in Pe with Gain in Ke ? Lately i discovered that i was not familiar with basic physics -...
Even the average student can assume in cases where a tennis ball falls freely or is hit that Ke = Pe.
The question is why do we take it as if they are equal?
When the 21-year old John Nash wrote his 27-page dissertation outlining his "Nash Equilibrium" for strategic non-cooperative games, the impact was enormous. On the formal side, his existence proof was one of the first applications of Kakutani's fixed-point theorem later employed with so much...
I will answer your question with a simple quote :
"As far as the laws of mathematics refer to reality, they are not certain. As far as the laws of mathematics are certain, They do not refer to reality"
Albert Einstein