Question

Potential Energy Curve \[U\] as a function of position of a particle is shown. The particle has total mechanical energy \[E\] of \[3.0joules\] . Then select the correct alternative.
(A). It can never be present at \[x=0m\]
(B). It can never be present at \[x=5m\]
 (C). at \[x=2\] its kinetic energy is \[0J\]
 (D). at \[x=1\] its kinetic energy is \[3J\]

Answer 1

Hint: The given graph shows the relationship between potential energy and the position of an object with respect to the origin. Potential energy varies unevenly throughout the graph. Using the given mechanical energy, we can calculate kinetic energy for given points and check the options.

Formula used: \[M=K+U\]

Complete step by step answer:
Potential energy is the energy possessed by a body by virtue of its position. Potential energy is the energy stored in a body due to its state, position or arrangement.
Kinetic energy is the energy possessed by a body by virtue of its motion.
Mechanical energy is the sum of kinetic energy and potential energy of a body.
 \[M=K+U\]
 Here, \[K\] is kinetic energy
 \[U\] is potential energy

 

The above graph shows a relation between potential energy of an object and its distance from the origin. According to the graph, the object has the highest potential energy of \[6J\] at \[x=0\] and minimum potential energy of \[-4J\] at \[x=5\] . We can observe that potential energy increases and decreases unevenly throughout the graph.

Given,
 \[\begin{align}
  & M=3J \\
 & \Rightarrow K+U=3J \\
\end{align}\]
The kinetic energy at \[x=0\] from the above eq will be-
 \[\begin{align}
  & K+6=3 \\
 & \Rightarrow K=-3J \\
\end{align}\]
But kinetic energy can only take 0 or positive values. Therefore, we can say that, object cannot exist at \[x=0\] . Also, every object has a tendency to acquire a minimum energy state because the more energy is stored in the body, the more unstable it is.
At point \[x=2\] , the kinetic energy of the body is-
 \[\begin{align}
  & K+0=3 \\
 & \Rightarrow K=3J \\
\end{align}\]
At point \[x=1\] the kinetic energy of the body is-
 \[\begin{align}
  & K+2=3 \\
 & \Rightarrow K=1J \\
\end{align}\]
Since the object has a very unstable configuration and negative kinetic energy at \[x=0\] .

So, the correct answer is “Option A”.

Note: The lower the potential energy of a body, the more stable it is. Therefore, potential energy at \[x=5\] is the most stable configuration of the object. Negative potential energy means work is being done by the object. Positive potential energy means work is being done on the object.