Question

show that Total energy of a body performing vertical circular motion is conserved. ​

Answer 1

Energy conservation in vertical circular motion:

Let's assume that a body is projected with limiting velocity [i.e. √(5gr)] , where r is radius of vertical circular motion.

Now, with calculations we can say :

• Velocity at top position is √(gr).

Now, at lowest position:

$TE = PE + KE$

$\implies TE = 0 + \dfrac{1}{2} m {( \sqrt{5gr}) }^{2}$

$\implies TE = \dfrac{5mgr}{2}$

Now, at highest position:

$TE = PE + KE$

$\implies TE = mg(2r) + \dfrac{1}{2} m {( \sqrt{gr}) }^{2}$

$\implies TE = 2mgr + \dfrac{mgr}{2}$

$\implies TE = \dfrac{5mgr}{2}$

So, total energy is conserved in vertical circular motion.

[HENCE PROVED]