Given in Figure, are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.
The total energy is given by E = K.E. + P.E.
K.E. = E – P.E.
Kinetic energy can never be negative. The particle cannot exist in the region, where K.E. would become negative.
(a) For the region x = 0 and x = a, potential energy is zero. So, kinetic energy is positive. For, x > a, the potential energy has a value greater than E. So, kinetic energy becomes zero. Thus the particle will not exist in the region x > a.
The minimum total energy that the particle can have in this case is zero.
(b) For the entire x-axis, P.E. > E, the kinetic energy of the object would be negative. Thus the particle will not exist in this region.
(c) Here x = 0 to x = a and x > b, the P.E. is greater than E, so the kinetic energy is negative. The object cannot exist in this region.
(d) For x = -b/2 to x =-a/2 and x = a/2 to x = b/2 . Kinetic energy is positive and the P.E. < E. The particle is present in this region.Answered by Pragya Singh | 1 year ago
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