Question

An object of mass 'm' is allowed to fall freely from point A as shown in the figure. Calculate the total mechanical energy of the object at :
(i) Point A
(ii) Point B
(iii) Point C
(iv) State the law which is verified by your calculations in parts (i), (ii) and (iii).

Answer 1

Point A :

Kinetic energy is zero i.e. $K=0$

Potential energy $U=mg(x+y)$

Total energy $T=U+K=mg(x+y)$

Point B :

Velocity $v=\sqrt{2g\left(x\right)}$

Kinetic energy $K=\frac{1}{2}m{v}^2=mg\left(x\right)$

Potential energy $U=mg\left(y\right)$

Total energy $T=U+K=mg(x+y)$

Point C :

Velocity $v=\sqrt{2g(x+y)}$

Kinetic energy $K=\frac{1}{2}m{v}^2=mg(x+h)$

Potential energy $U=0$

Total energy $T=U+K=mg(x+y)$

The above parts verifies the law of conservation of energy.