What is the acceleration of a particle at x=10 m if the mass of the particle is 0.2 kg ? the  particle is moving along x axis with the potential energy U(x)= 8x^2-2x^4

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Work is given by the product of the force and distance. The work done contributes to an increase in potential energy.

Work = -delta U.

Force* distance = -delta U

Here we have the function of the potential energy given as U(x) = 8*x^2 - 2*x^4.

For an infinitesimally small...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

Work is given by the product of the force and distance. The work done contributes to an increase in potential energy.

Work = -delta U.

Force* distance = -delta U

Here we have the function of the potential energy given as U(x) = 8*x^2 - 2*x^4.

For an infinitesimally small change in distance

d/dx (Force* distance) = -U'(x)

Force = -U'(x)

U'(x) = 16x - 8x^3

At x = 10,

U'(x) = 16*10 - 8*1000

=> 160 - 8000

=> -7840

=> Force = - (-7840)

=> Force = 7840

So the force at this point is 7840.

Force is the product of the mass and acceleration. We know that the mass is 0.2 kg.

Therefore the acceleration is 7840 / 0.2 = 39200 m/s^2

Approved by eNotes Editorial Team