Chapter 10 - Interactions and Potential Energy - Exercises and Problems - Page 257: 32

At $y=0$: $F_y = 0$ At $y=1~m$: $F_y = -12~N$ At $y=2~m$: $F_y = -48~N$

$U = 4y^3~J$ We can find an expression for $F_y$: $F_y = -\frac{dU}{dy}$ $F_y = -12y^2~N$ We can find $F_y$ at $y = 0$: $F_y = -12y^2~N$ $F_y = -(12)(0)^2~N$ $F_y = 0$ We can find $F_y$ at $y = 1$: $F_y = -12y^2~N$ $F_y = -(12)(1)^2~N$ $F_y = -12~N$ We can find $F_y$ at $y = 2$: $F_y = -12y^2~N$ $F_y = -(12)(2)^2~N$ $F_y = -48~N$