Question

Given in Fig. 6.11 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

Explanation:

(a) x > a

The relation which gives the total energy:

E = P.E + K.E

K.E. = E – P.E

K.E of the body is a positive quantity and the region where K.E is negative, the particles does not exist.

For x > a, the potential energy V0 is greater than the total energy E. Hence, the particle does not exist here. The minimum total energy is zero.

(b) All regions

The total energy in all regions is less than the kinetic energy. So the particles do not exist here.

(c) x < b and x > a; =V1

K.E is positive in the region between x > a and x < b. –V1 is the minimum potential energy. K.E = E – (-V1) = E + V1. For the K.E to be positive, total energy must be greater than –V1.

(d) $\frac{-b}{2}$ < x < $\frac{a}{2}$; $\frac{a}{2}$ < x < $\frac{b}{2}$; -V1

For the given condition, potential energy is greater. So in this region, the particles do not exist. –V1 is the minimum potential energy. K.E = E + V1. For the K.E to be positive, total energy must be greater than –V1. The particle must have a minimum total K.E of –V1.

Answer 2

Answer:

EEMDNESIEMSIENSKIDKUDKEISUIEAP Explanation: