Question

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

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

Answer 1

The correct option is A The mechanical energy of system is $69J$.

• Since the force applied on the body is conserved ,therefore its total mechanical energy is going to be same at all values of 'x'.
• Therefore we can calculate its mechanical energy at any value of 'x'.
  

we do it at $x=5m$

Total energy =kinetic energy+potential energy.

$=50+[15+(x-3{)}^2]$ at $x=5$

$=50+[15+(5-3{)}^2]$

$=50+[15+4]$

$=69J$