Question

A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in the figure The kinetic energy of the object at the origin is 12J. The system is conservative, and there is no friction. What will be the kinetic energy at 2. 0 m along the x-axis?

Answer 1

The system is conservative.

From the graph, the potential energy at the origin = 22 joules

Kinetic energy at the origin = 12 joules

Therefore,

$\begin{gathered} \text{ Kinetic energy + potential energy =22 + 12 = 34} \\ \text{This total will remain constant all through the graph} \end{gathered}$

The kinetic energy at 2.0m along the x-axis can be calculated as follows

let

x = kinetic energy at 2.0m

The potential energy at 2.0m = 10 joule

$\begin{gathered} 34=10+x \\ 34-10=x \\ x=24\text{ joules} \end{gathered}$

Kinetic energy at 2.0m along the x-axis = 24 Joules