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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?

Respuesta :

Answer:

[tex]F_1=F_2[/tex]

Step-by-step explanation:

  Given that

For system 1

[tex]U_1(x)=Cx^2+Bx^3[/tex]

For system 2

[tex]U_2(x)=A+Cx^2+Bx^3[/tex]

A is positive quantity

We know that

Force F

[tex]F=\dfrac{dU}{dx}[/tex]

For system 1

[tex]\dfrac{dU}{dx}=2Cx+3Bx^2[/tex]

[tex]F_1=2Cx+3Bx^2[/tex]

For system 2

[tex]\dfrac{dU}{dx}=0+2Cx+3Bx^2[/tex]

[tex]F_2=2Cx+3Bx^2[/tex]

[tex]F_1=2Cx+3Bx^2[/tex]

[tex]F_2=2Cx+3Bx^2[/tex]

[tex]F_1=F_2[/tex]

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

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