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A graph of potential energy V(x) verses ...

A graph of potential energy V(x) verses x is shown in figure .A particle of energy `E_(0)` is executing motion in it . Draw graph of velocity and kinetic energy verses x for one complete cycle AFA.

Text Solution

Verified by Experts

We know that
Total `E = K +U `
`E = K+V(x) " " ( :. U = V(x))`
`K = E_(0)-V(x) " " ( :. E =E_(0))`
at A , x = 0 ,V(x) = `E_(0)`
` :. K =E_(0)-E_(0)=0`
at B , `V(x) lt E_(0)`
` :. K =E_(0)` (Maximum)
K=0
At F,
the variation is as below ,

Velocity versus x graph :
As `KE =1/2 mv^(2)`
` :. ` At A and F , where KE = 0 , v = 0
At C and d , KE is maximum .Therefore , v is `pm` max .
At B . KE is positive but not maximum .
Therefore , v is `pm ` some value ( `lt` max)
The variation is shown in the diagram .
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