Half a coconut of mass $0.25$ kg is suspended from a tree branch by a light piece of string of fixed length $0.4$ m. A gust of wind displaces the bob from its equilibrium position and the center of mass of the coconut rises $20$ cm above its rest position.
a) What is the potential energy as it reaches its maximum height?
b) What is the kinetic energy of the coconut at its maximum height and when it passes through the equilibrium position?
c) What is the maximum speed of the coconut?
d) What is the maximum tension of the string?
Can someone please help me with these questions? I am desperate...
a) potential energy $= mgh$
b) energy is conserved.
c) since energy is conserved... $\frac 12 mv^2 + mgh$ is constant.
d) This is the trickiest part, cicular motion requires centripetal acceleration = $\frac {v^2}{r}$ this is added to the tension on the string from gravity.
I suppose for part d) you might also consider the tension on the string before the system is set into motion.