Question

the potential energy of a particle moving along the x-axis is given by you is equals to 8* X square + 2*X to the power 4 where you is in joules and X is in metres if the total mechanical energy is 9 joules find the limit of motion

Answer 1

Potential energy of the system is given as

$U = 8x^2 + 2x^4$

its mechanical energy is also given as

$E = 9J$

now when whole mechanical energy will convert to Potential energy then it will be the limit of motion

$9 = 8x^2 + 2x^4$

$2x^4 + 8x^2 - 9 = 0$

by solving above equation we have

$x^2 = 0.91$

$-0.95 < x < + 0.95$

so it will move from x = -0.95 m to x = + 0.95 m

Answer 2

Answer:

Potential energy of the system is given as

its mechanical energy is also given as

now when whole mechanical energy will convert to Potential energy then it will be the limit of motion

by solving above equation we have

so it will move from x = -0.95 m to x = + 0.95 m

Explanation: