Potential Energy P.E. explained with examples

Potential energy is the energy that an object possesses due to its position or state. It is defined as the work done by a conservative force in moving an object from one position to another. It is typically represented by the symbol "U" and is measured in joules (J).

The formula for potential energy is:

U = mgh

where:

U is the potential energy (in joules, J)

m is the mass of the object (in kilograms, kg)

g is the acceleration due to gravity (in meters per second squared, m/s^2)

h is the height of the object above a reference point (in meters, m)

In other words, potential energy is proportional to the mass of an object, the acceleration due to gravity, and the height of the object above a reference point. The greater the mass, height, and gravitational acceleration of an object, the greater its potential energy.

For example, if a book of mass 2 kg is placed on a shelf 3 meters above the ground, the potential energy of the book can be calculated using the formula:

U = mgh

U = 2 kg × 9.81 m/s^2 × 3 m

U = 58.86 J

So, the potential energy of the book on the shelf in this case would be 58.86 joules.

Another example where the formula for potential energy can be used is in a scenario where a spring of spring constant 100 N/m is compressed by 0.1 meters. If the mass attached to the spring is 0.5 kg, we can calculate its potential energy using the formula:

U = (1/2)kx^2

U = (1/2) × 100 N/m × (0.1 m)^2

U = 0.5 J

So, the potential energy of the spring-mass system when the spring is compressed by 0.1 meters would be 0.5 joules.

In another scenario, a block of mass 2 kg is lifted to a height of 5 meters above the ground and held there by a person. The potential energy of the block is given by:

U = mgh

U = 2 kg × 9.81 m/s^2 × 5 m

U = 98.1 J

So, the potential energy of the block in this case would be 98.1 joules. When the person releases the block, its potential energy is converted to kinetic energy, which can be calculated using the formula:

K = (1/2)mv^2

Assuming that there is no air resistance, the velocity of the block just before it hits the ground can be calculated by equating the kinetic energy to the potential energy:

K = U

(1/2)mv^2 = mgh

v^2 = 2gh

v = √(2gh)

v = √(2 × 9.81 m/s^2 × 5 m)

v = 9.9 m/s

So, the velocity of the block just before it hits the ground would be 9.9 m/s.