A single conservation force F(x) acts on a 1.0 kg particle that moves along an x-axis. The potential energy U(x) associated with F(x) is given by:
U(x) = -4x e^(-x/4) J,
where x is in meters. At x = 5.0m the particle has a kinetic energy of 2.0J.
a) What is the mechanical energy of the system?
b) Make a plot of U(x) as a function of x for 0 ≤ x ≤ 10 m, and on the same graph draw the line that represents the mechanical energy of the system
c) Use part b to find least value of x
d) Use part b to find greatest value of x between which the particle can move.
e) Use part b to determine the maximum kinetic energy of the particle
f) Find the value of x at which maximum kinetic energy occurs.
g) Determine the equation for F(x) as a function of x.
h) For what (finite) value of x does F(x) = 0?
The solution gives a detailed response including several illustrative graphs.