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 $E_{\text {mech }}=8\, J$, 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 $x=x_{3}, K . E .=4 J$

Answer 1

Answer: (B)

$E_{\text {mech }}=8 J$
(A) at $x > x_{4}, U=$ constant $=6\, J$
$K=E_{\text {mech. }}-U=2\, J=$ constant
(B) at $x< x_{1}, U=$ constant $=8\, J$
$K=E_{\text {mech. }}-U=8-8=0\, J$
Particle is at rest.
(C) At $x=x_{2}, U=0$
$ \Rightarrow E_{\text {mech. }}=K=8\, J$
$KE$ is greatest, and particle is moving at fastest speed.
(D) At $x=x_{3}, U=4 \,J$
$U+K=8\, J $
$K=4 \,J$