Question

A single conservative force $F(x)$ acts on a particle that moves along the $x$-axis. The graph of the potential energy with $x$ is given. At $x=5\, m$, the particle has a kinetic energy of $50 \,J$ and its potential energy is related to position ' $x$ ' as $U=15+(x-3)^{2}$ Joule, where $x$ is in meter. Then :

• A. The mechanical energy of system is 69
• B. The mechanical energy of system is 19 J
• C. At $x=3$, the kinetic energy of particle is minimum
• D. The maximum value of kinetic energy is 54 J

Answer 1

Answer: (A), (D)

$U =15+(x-3)^{2} $
$U(5) =19 \, \&\, K E(5)=50$
Total mechanical energy $=50+19=69 \,J$
$U_{\text {min. }} \equiv U(x-3) =15 \,J $
$K E_{\max .} =69-U_{\min .}=69-15=54 \,J$