Question

Obtain expression for energy at different positions in the vertical circular motion. Hence show that total energy in vertical circular motion is constant.

OR

Show that total energy of a body performing vertical circular motion is conserved.

Answer 1

Expression for energy at different points in V.C.M:

i. Consider a particle of mass m revolving in a vertical circle of radius r in anticlockwise direction.

ii. When the particle is at highest point H:

Equation (1) represents energy of particle at the highest point in V.C.M.

iii. When particle is at lowest point L:

P.E = 0 [\(\because\) At lowest point, h = 0]

Equation (2) represents energy of particle at lowest point in V.C.M

iv. When the particle is at midway point in V.C.M:

P.E = mgh = mgr [\(\because\) h = r]

Equation (3) represents total energy of particle at midway position in V.C.M

v. From equation (i), (ii) and (iii), it is observed that total energy at any point in V.C.M is 5/2 mgr, i.e., constant.

Hence, total energy of a particle performing vertical circular motion remains constant.