A simple pendulum is an example of a system in Simple Harmonic Motion, using conservation laws find a) the greatest speed of the bob and b) the magnitude of speed at a height of 1.0cm above the minimum point. Given it starts at rest, at a height of 20cm.
As this is an isolated system and a simple pendulum starting at rest, at maximum height, all the energy is in potential energy. The known equation for potential energy is simply mgh (mass x acceleration due to gravity x height) and at minimum height this can be set as potential energy = 0, meaning all energy must be in the form of kinetic. The equation for kinetic energy is assumed known as (1/2)mv2 ( 0.5 x mass x magnitude of the velocity2), to find the answers the student must find how much energy is in each form. One notes how mass is not stated but student will find it cancel.With all equations and concepts outlined one simply calculates the numbers, for part a) all energy is converted from potential to kinetic, thus (1/2)mv2 = mgh, simply rearranged for speed as v=(2gh)0.5= (2 * 9.81 * 0.2) = 2.0 ms-1. In part b) there still exists some energy in potential as well as kinetic so the student sets up the equation; mgh = (1/2)mV2 + mgH, the capitals are to highlight how the value for velocity is not that from before, and that the initial and final heights are not the same. Again the mass cancels and the equation rearranges to V = (2g(h-H))0.5 = (2 * 9.81 * (0.2 -0.01))0.5 = 1.9 ms-1. Units required with both answers as well as given to the same significant figures as the question.
