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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 versus x for one complete cycle AFA.

Text Solution

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Total energy `E_(0) = KE +PE`
or `E_(0) = KE +V(x)`
or `KE = E_(0) - V(x)`
At A , `V(x) = E_(0) `and KE = 0 , so v = 0
Figures (a) and (b) show the graph of velocity and KE versus x for complete cycle AFA .

At B ,`V(x) lt E_(0)` and KE is positive but not maximu
At C and D , V(x) = 0 and KE = maximum ,
` v = pm ` maximum
At F , `V(x) =E_(0) `and KE = 0 , so v = 0
Figures (a) and (b) show the graph of velocity and KE versus x for one complete cycle AFA .
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Knowledge Check

  • The potential energy function for a particle executing linear SHM is given by V(x)= 1/2kx^2 where k is the force constant of the oscillator. For k = 0.5 Nm^(-1) , the graph of V(x) versus x is shown in the figure A particle of total energy E turns back when it reaches x=pmx_m .if V and K indicate the potential energy and kinetic energy respectively of the particle at x= +x_m ,then which of the following is correct?

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