Answer to Question #122771 in Classical Mechanics for Umar Farooq

Question

A stone of mass $10$g placed at the top of a tower $50$m high is allowed to fall freely. Show that law of conservation of energy is holds.

Answer 1

Given, Mass of stone is $M=10g$ ,Height of the tower is $H=50m$ .

Initially, energy on system is just form of potential in particularly gravitional potential energy,thus

$$E=MgH$$

Now, consider at any arbitrary time ,the stone reach to distance $X$ and velocity is $v$ ,thus kinetic energy at that moment is

$$K=\frac{1}{2}Mv^2$$

Potential energy is

$$U=Mg(H-X)$$

Also, due to free fall under gravity

$$v^2=2gX$$

Hence, considering the above fact energy on the system will be

$$K+U\\ \implies K+ U=MgH=E$$

We are done.