Question

In the given 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.

Answer 1

We know that total energy E = K.E. + P.E. or K.E. = E – P.E. and kinetic energy can never be negative.The object can not exist in the region, where its K.E. would become negative.

1. In the region from x = 0 to x = a, the potential energy is zero. Thus, the kinetic energy here is positive. . However, in the region x > a, the potential energy has a value V₀ > E; therefore, kinetic energy becomes negative. As a result, the object cannot exist beyond x>a.
    
2. The object cannot exist in any region because of its potential energy V₀ > E in all regions.
3. In these regions, from x = 0 to x = a and x > b, the potential energy (V₀) is greater than the total energy E of the object. Therefore, kinetic energy becomes negative, and the object cannot be present at x < a and x > b.
4. The object can not exist in the regions  `-b/2 < x <-a/2 and a/2 < x<b/2`. Because in this region, P.E. > E.