Question

You are about to swing on a rope from a tree branch that is 8m above the ground and at the bottom of that swing you are 1m above the ground. Draw a diagram labelling before and after positions, velocities and energies.

Answer 1

The path is circulur and the forces are conservative and hence conservation of mechanical energy is valid.

INITIAL: energy=mgH where H is 8m
FINAL : energy=mgh+mv^2/2=mgH where h is 1m
velocity=sqrt(2g(H-h)) [using the energy eqn as above]
***ALSO THE VELOCITY IS TANGENTIAL AT THE BOTTOM****

Answer 2

Thank you!