Question

A single conservative force $F\left(x\right)$ acts on a $1.0kg$ 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 $x=5.0m$ the particle has a kinetic energy of $20J$.

What is the mechanical energy of the system?

• A. $59J$
• B. $29J$
• C. $49J$
• D. $35J$

Answer 1

Answer: (C)

$49J$

Potential energy at $x=5.0m$ is

$U=20+{(5-2)}^2=29J$

$\therefore$ Mechanical energy

$E=K+U=20+29=49J$