A body weighing 10 kg has a velocity of 6 m/s, after one second of starting from the mean position. If the time period of SHO is 6 s, find the kinetic energy, potential energy and total mechanical energy of SHO.
Answers
Kinetic energy = 180 J
Potential energy = 540 J
Total mechanical energy = 720 J
Explanation:
=> It is given that,
mass of a body, m = 10 kg
velocity of a body, v = 6 m/s
time period of SHM, t = 6 s
time, t = 1s
=> Kinetic energy, K.E. :
K.E = 1/2 mv²
= 1/2 * 10 * ( 6 )²
= 1/2 * 10 * 36
= 180 J
=> Total energy, T.E :
now velocity, v = αω cos ωt
6 = αω cos (2π/T)t
6 = αω * 1/2
αω = 12
As T.E. = 1/2 mω²α²
= 1/2 * 10 * (12)²
= 1/2 * 10 * 144
= 720 J
=> Potential Energy, P.E. :
P.E. = T.E. - K.E.
= 720 - 180
= 540 J
Learn more:
Q:1 Derive the expression for the kinetic and potential energy of harmonic oscillator.Hence show that total energy is conserved in SHM. Draw graphs for (1) energy vs time and (2)energy vs displacement
Click here: https://brainly.in/question/2693523
Q:2 Obtain expressions for kinetic energy, potential energy and total energy of a particle performing linear S.H.M.
Click here: https://brainly.in/question/6497036
hope this helps...............
