The force acting on an object is given by Fx = a/x2. At x = 4.9 m, the force is

Question

The force acting on an object is given by Fx = a/x2. At x = 4.9 m, the force is known to point in the -x direction and have a magnitude of 27 N. Determine the potential energy associated with this force as a function of x, assuming we assign a reference value of -9 J at x = 2 m for the potential energy.
U(x) =




the answer should look something like this ( -567/x + 272.5) this is an answer form another version and that question was:
The force acting on an object is given by Fx = a/x2. At x = 4.5 m, the force is known to point in the -x direction and have a magnitude of 28 N. Determine the potential energy associated with this force as a function of x, assuming we assign a reference value of -11 J at x = 2 m for the potential energy.

Explanation / Answer

It goes like this

1. x = 4.9 m

First you solve for "a" from Fx = a/x^2 = -27N

a = (-27N)(x^2) = (-27N)(4.9m)^2 = -648.27 N.m^2

2. x = 2 m , Ux = -9J

then you use the potential energy equation Ux = -int (F*dx) = -9 J

Ux = -int [(a/x^2)*dx] = -a*int (1/x^2)*dx] = -a(-1/x) + C = a/x + C

Ux = a/x + C = -9 J

C = -9 J -(a/x) = -9 J -(-648.27 N.m^2/2m) = -9 J -(-324.135) = -9 J + 324.135 J = 315.135 J

And with all of this the potential energy associated with this force as a function of x is:

Ux = (-648.27/x) + 315.135 J

that's your answer! Good luck!

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