Chapter 8, Problem 81P

A particle can move along only an x axis, where conservative forces act on it (Fig. 8-66 and the following table). The particle is released at x = 5.00 m with a kinetic energy of K = 14.0 J and a potential energy of U = 0. If its motion is in the negative direction of the x axis, what are its (a) K and (b) U at x = 2.00 m and its (c) K and (d) U at x = 0? If its motion is in the positive direction of the x axis, what are its (e) K and (f) U at x = 11.0 m, its (g) K and (h) U at x = 12.0 m, and its (i) K and (j) U at x = 13.0 m? (k) Plot U(x) versus x for the range x = 0 to x = 13.0 m.

Figure 8-66 Problems 81 and 82.

Next, the particle is released from rest at x = 0. What are (l) its kinetic energy at x = 5.0 m and (m) the maximum positive position x_max it reaches? (n) What does the particle do after it reaches x_max?

Range	Force
0 to 2.00 m	${\stackrel{\to }{F}}_1=+(3.00\text{ N) <mover accent="true"> i <mo> ^ </mo> </mover>}$
2.00 m to 3.00 m	${\stackrel{\to }{F}}_2=+(5.00\text{ N) <mover accent="true"> i <mo> ^ </mo> </mover>}$
3.00 m to 8.00 m	$\stackrel{\to }{F}=0$
8.00 m to 11.0 m	${\stackrel{\to }{F}}_3=+(4.00\text{ N) <mover accent="true"> i <mo> ^ </mo> </mover>}$
11.0 m to 12.0 m	${\stackrel{\to }{F}}_4=+(1.00\text{ N) <mover accent="true"> i <mo> ^ </mo> </mover>}$
12.0 m to 15.0 m	$\stackrel{\to }{F}=0$