Question

Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C and D in which the relation between potential energy V, kinetic energy (K) and total energy E is as given below:

Region A : V > E
Region B : V < E
Region C : K > E
Region D : V > K

State with reason in each case whether a particle can be found in the given region or not.

Answer 1

We know that

Total energy E = PE + KE

⇒ E = V + K  ......(i)

For region A Given, V > E, From equation (i)

K = E – V

As V > E ⇒ E – V < 0

Hence, K < 0, this is not possible.

For region B Given, V < E ⇒ E – V > 0

This is possible because total energy can be greater than PE(V)

For region C Given, K > E ⇒ K – E > 0

From equation (i) PE = V = E – K < 0

This is possible because PE can be negative.

For region D Given, V > K

This is possible because for a system PE (V) may be greater than KE (K).