Given in Fig, are examples of some potential energy functions in one

1.	Given in Fig, 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.
Answer» (a) We know that Total energy E = KE + PE, kinetic energy can never be negative. In the region between x = 0 & x = a. Potential energy is ‘0’. So, kinetic energy y is positive. In region x > a the potential energy has a value greater than ‘E’. So kinetic energy will be negative in this region. Hence the particle cannot be present in the region x > a. (b) Here PE > E, the total energy of the object and as such the kinetic energy of the object would be negative. Thus object cannot be present in any region on the graph. (c) Here x = 0 to x = a & x > b, the P E is more then E so, K E is negative. The particle cannot be present in these portions. (d) The object cannot exist in the region between x =\(\frac{-b}{2}\) to x =\(\frac{-a}{2}\) & x =\(\frac{-a}{2}\) to x =\(\frac{-b}{2}\) Because in this region P E > E.

Given in Fig, 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.

Answer»

(a) We know that Total energy E = KE + PE, kinetic energy can never be negative. In the region between x = 0 & x = a.

Potential energy is ‘0’. So, kinetic energy y is positive. In region x > a the potential energy has a value greater than ‘E’. So kinetic energy will be negative in this region. Hence the particle cannot be present in the region x > a.

(b) Here PE > E, the total energy of the object and as such the kinetic energy of the object would be negative. Thus object cannot be present in any region on the graph.

(c) Here x = 0 to x = a & x > b, the P E is more then E so, K E is negative. The particle cannot be present in these portions.

(d) The object cannot exist in the region between

x =\(\frac{-b}{2}\) to x =\(\frac{-a}{2}\) & x =\(\frac{-a}{2}\) to x =\(\frac{-b}{2}\)

Because in this region P E > E.

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