Question

Given below is the plot of a potential energy function $U(x)$ for a system, in which a particle is in one dimensional motion, while a conservative force $F(x)$ acts on it. Suppose that $E_{\text{mech }}=8J$, the incorrect statement for this system is:

• A. at $x>x_4,K.E.$ is constant throughout the region.
• B. at $x<x_1,K.E$. is smallest and the particle is moving at the slowest speed.
• C. at $x=x_2,K.E$. is greatest and the particle is moving at the fastest speed.
• D. at $x=x_3,K.E.=4J$

Answer 1

Answer: (B)

$E_{\text{mech }}=8J$
(A) at $x>x_4,U=$ constant $=6J$
$K=E_{\text{mech. }}-U=2J=$ constant
(B) at $x<x_1,U=$ constant $=8J$
$K=E_{\text{mech. }}-U=8-8=0J$
Particle is at rest.
(C) At $x=x_2,U=0$
$\Rightarrow E_{\text{mech. }}=K=8J$
$KE$ is greatest, and particle is moving at fastest speed.
(D) At $x=x_3,U=4J$
$U+K=8J$
$K=4J$