# Homework Help: Potential Energy - Work Done etc

1. Oct 14, 2012

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1. Two children of mass 40 kg and 50 kg are holding on to the ends of a rope which passes over a thick horizontal branch of a tree. The parts of the rope on either side of the branch are vertical and the heavier child is moving downwards. A model is to be used in which the children may be considered as particles, and in which the rope is light and inextensible and is moving freely in a smooth groove on the branch. when the heavier child is moving at 2 m s^-1, she lets go of the rope. Calculate the further upward distance moved by the other child before falling back to the ground.
The motion described began with both children stationary. Calcuylate the distance they travelled before one let go of the rope.

2. A particle is at rest at the apex A of a smooth fixed hemisphere whose base is horixontal. Thhe hemisphere has centre O and radius a. The particle is then displaced very slightly from rest and moves on the surface where angle AQP=θ the particle has speed v. Find an expression for v in terms of a, g and θ.