Question

A single conservative force $F\left(x\right)$ acts on a $1.0-kg$ particle that moves along the x-axis. The potential energy $U\left(x\right)$ is given by $U\left(x\right)=20+(x-2{)}^2$ where x is in meters. At $x=5.0$ m, the particle has a kinetic energy of $20J$.What is the mechanical energy of the system?

• A. $35J$
• B. $64J$
• C. $86J$
• D. $49J$

Answer 1

The correct option is D $49J$

$U\left(x\right)=20+{(x-2)}^2$

at $x=5m$

$\Rightarrow U\left(x\right)=20+{(5-2)}^2$

$=29J$

$\Rightarrow KE=20J$

Mechanical energy $=PE+RE$

$=20+29$

$=49J.$

Hence, the answer is $49J.$