Question

A potential energy function for system 1 is given by U1(x)=Cx2+Bx3. The potential energy function for system 2 is given by U2(x)=A+Cx2+Bx3, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

Answer 1

`F_1=F_2`

Explanation:

Given that

For system 1

`U_1(x)=Cx^2+Bx^3`

For system 2

`U_2(x)=A+Cx^2+Bx^3`

A is positive quantity

We know that

Force F

`F=(dU)/(dx)`

For system 1

`(dU)/(dx)=2Cx+3Bx^2`

`F_1=2Cx+3Bx^2`

For system 2

`(dU)/(dx)=0+2Cx+3Bx^2`

`F_2=2Cx+3Bx^2`

`F_1=2Cx+3Bx^2`

`F_2=2Cx+3Bx^2`

`F_1=F_2`

So from above equations we can say that force on both system is equal at given value of x.