Chapter 7, Problem 87E

(a)

To determine

To show that $U\left(x\right)$ can be written as $U\left(x\right)=\frac{\alpha }{x_0^2}\left[{\left(\frac{x_0}{x}\right)}^2-\frac{x_0}{x}\right]$ and calculate $U\left(x_0\right)$ by locating the point $x_0$ on the graph of $U\left(x\right)$.

(b)

To determine

The speed of the proton as a function of time and graph the $v\left(x\right)$ versus $x$.

(c)

To determine

The value of $x$ at which the speed of the proton is maximum and the value of maximum speed.

(d)

To determine

The force on the proton at the point in part (c).

(e)

To determine

The point $x_1=\frac{3\alpha }{\beta }$ on the graph of $U\left(x\right)$ and the $v\left(x\right)$ at this point.

(f)

To determine

The maximum and minimum value of $x$ reaches during the motion.