A rock of mass 13 kg is tied to a string of length 2.9 m, with the other end of

Question

A rock of mass13kg is tied to a string of length2.9m, with the other end of the string fastened to the ceiling of a tall room. While hanging vertically, the rock is given an initial horizontal velocity of2.1m/s.

b) What is the potential energy of the rock? (Use the following as necessary:m,g, andh.)

What is the initial kinetic energy of the rock?

(c) If the rock swings to a heighthabove its initial point, what is its potential energy? (Use the following as necessary:m,g, andh.)

What is its total mechanical energy at that point?

(d) How high will the rock swing? Express your answer in terms of the angle?that the string makes with the vertical when the rock is at its highest point.

(e) Make qualitative sketches of the kinetic energy and potential energies as functions of heighth. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

a) The logical place to choose the origin is at the bottom of the arc (so thatpotential energyis 0 here)
b)initial kinetic energyis mv0^2 / 2, initial potential energy is 0
c) potential energy is mgh. Energy is conserved, so total energy is still 1/2 * mv0^2
h) Maximum hight will be when mgh = 1/2 mv^2.

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