Question

A potential energy function for a system in which a two-dimensional force acts is of the form U = 3x6y − 5x. Find the force that acts at the point (x, y). (Use the following as necessary: x and y.)

Answer 1

Answer:

Force, $F=((-18x^5y+5)i+(-3x^6)j)\ N$

Explanation:

Given that,

A potential energy function for a system in which a two-dimensional force acts is of the form of :

$U=3x^6y-5x$

We need to find the force that acts at the point (x, y). The force in 2 dimensional with components is given by :

$F=(\dfrac{-dU}{dx},\dfrac{-dU}{dy})\\\\F=(\dfrac{-d(3x^6y-5x)}{dx},\dfrac{d(3x^6y-5x)}{dy})\\\\F=(-(18x^5y-5)),(-(3x^6))\\\\F=((-18x^5y+5)i+(-3x^6)j)\ N$

So, the force acting at the point (x,y) is $((-18x^5y+5)i+(-3x^6)j)\ N$. Hence, this is the required solution.