Question
Mon February 25, 2013 By:
 

can an object have momemtum if its mechanical energy is zero? also state when can potential energy be negative? prove mathematically the conservation of energy in a simple pendulum?how can u justify that the motion of the pendulum is a simple harmonic motion?

Expert Reply
Tue February 26, 2013
Yes it can be: Eg. the kinetic energy is always positive but if potential energy is negative and equal, its total mechanical energy will be 0 but it will have a momentum.
 
Potential energy is negative when, the body is in a restricted motion, ie when we need to supply energy to the body to get it to a space of no potential energy.
 
THe motion of simple pendulum can be justified as simple harmonic motion if we prove its differential equation to be:
d2x/dt2 = -w2x
 
Conservation of energy in simple pendulum:
let the velocity of pendulum at center to be v
then it s mechanical energy would be: 1/2 mv2
its max height will be: H = v2/2g  (according to third equation of motion)
thus its energy will be mgH = 1/2mv2
hence the total energy is conserved.
 
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