Question

A single conservative force $F\left(x\right)$ acts on a $2.5\text{kg}$ particle that moves along $x-$axis. The potential energy $U\left(x\right)$ is given by $U\left(x\right)=(10+(x-4{)}^2)$ where $x$ is in meter. At $x=6\text{m}$, The particle has kinetic energy of $20\text{J}$. What is mechanical energy of the system?

• A. $34\text{J}$
• B. $45\text{J}$
• C. $48\text{J}$
• D. $49\text{J}$

Answer 1

The correct option is A $34\text{J}$

$\because$ According to law of conservation of energy, if no dissipative forces are present then the total mechanical energy remains conserved.
Here, sum of kinetic energy and potential energy remains conserved.
Potential energy, $U\left(x\right)$ at $(x=6\text{m})$
$=10+(6-4{)}^2$
$=10+4$
$U\left(6\right)=14\text{J}$
Kinetic energy, at $x=6\text{m},K{E}_{x=6}=20\text{J}$ (Given)
$\therefore$ Total mechanical energy of the system at $x=6\text{m},$
$=U\left(6\right)+KE\left(6\right)$
$=14\text{J}+20\text{J}$
$=34\text{J}$
Total mechanical energy of the system $=34\text{J}$