### Potential Energy

• Calculate the gravitational potential energy of a particle in various situations.

• Calculate the elastic potential energy of a particle attached to a stretched spring.

Potential Energy is the energy stored in an object due to its position.

Gravitational Potential Energy

$U = mgh$

Elastic Potential Energy

$U = \dfrac{1}{2} k x^2$

where k = stiffness(spring) constant

### Solved Example:

#### 31-2-01

Jack climbs a mountain via a short, steep trail. Jill ascends the same mountain via a long and considerably less steep path. Which of the following statements is true? Assume that Jack and Jill have the same mass.

Solution:

$\Delta U = mgh$, same h for both. So gravitational potential energy is same.

Reference: http://resources.seattlecentral.edu

### Solved Example:

#### 31-2-02

A compressed spring possesses _________. (RRC Group D Sept 2018 Shift II)

### Solved Example:

#### 31-2-03

A ball is dropped from a height h and rebounds to a height which is 80 % of the initial height. Find the ratio of final potential energy to the initial potential energy of the ball. (Airforce Group X Nov 2020)