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

Answer:

$F_1=F_2$

Step-by-step 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

$F=\dfrac{dU}{dx}$

For system 1

$\dfrac{dU}{dx}=2Cx+3Bx^2$

$F_1=2Cx+3Bx^2$

For system 2

$\dfrac{dU}{dx}=0+2Cx+3Bx^2$

$F_2=2Cx+3Bx^2$

$F_1=2Cx+3Bx^2$

$F_2=2Cx+3Bx^2$

$F_1=F_2$

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