Question

Kinetic energy of a particle on the surface of earth is E_(0) and the potential energy is - 2E_(0). (a) Will the particle escape to infinity ? (ii) What is the value of potential energy where speed of the particle becomes zero?

Answer 1

Here is your answer:

Explanation:

(i) Since, it is nagative, it will not escape to infinity.

(b) Ei=Ef⇒E0−2E0=0+U⇒U=−E0

(ii) Total mechanical energy = E0−2E0 =−E0.

Answer 2

Given that,

Kinetic energy of a particle on the surface of earth is

$K.E = E_{0}$

Potential energy of a particle on the surface of earth is

$P.E = -2E_{0}$

The potential energy at escape infinity is zero.

(a). We need to calculate the kinetic energy at escape infinity

Using conservation of energy

$E_{0}-2E_{0}=K.E_{f}+0$

$K.E_{i}+P.E_{i}=K.E_{f}+P.E_{f}$

Put the value into the formula

$K.E_{f}=-E_{0}$

The kinetic energy is negative so that's why particle will not escape to infinity .

(b). We need to calculate the potential energy where the speed of the particle becomes zero

Using conservation of energy

$K.E_{i}+P.E_{i}=K.E_{f}+P.E_{f}$

Put the value into the formula

$E_{0}-2E_{0}=0+P.E_{f}$

$P.E_{f}=-E_{0}$

Hence, (a). The kinetic energy is negative so that's why particle will not escape to infinity .

(b). The potential energy where the speed of the particle becomes zero is -E₀.