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The relation between kinetic and potential energy

The potential energy is the energy accumulated in an object by its location.

PE = mgh where, m - mass, g - acceleration due to gravity and h - height

The energy possessed by an object as a result of its motion is known as kinetic energy.

KE = \frac{1}{2} mv^2   Where, m-mass and v- velocity  

Energy cannot be destroyed, only converted from one form to another, according to the law of conservation of energy.

PE begins from 0 at the projection point and increases to a maximum value at a constant speed at maximum height.

KE begins at the projection point with a maximum value and decrease constantly to 0 at maximum height.

Total energy = PE + KE.

At the maximum height (when object dropped): PE = KE  

a)

Step 1: Measuring the total energy stored in the stone.

Given that

Mass of the stone m = 2 kg

Height of the building h = 20 m

Acceleration due to gravity g = 10 m/s^2


The potential energy existed until the stone was dropped.

KE = 0, since initial velocity   v = 0   

PE = mgh

PE = 2 * 10 * 20

PE = 400 joules

Initial potential energy = 400 joules  

Thus, total energy = KE + PE = 0 + 400 = 400 joules.

Step 2: Calculate the stone's height if potential energy equals kinetic energy.

PE = KE ...........................(1)

Set up equation for the height of the stone

Total energy = PE + KE

400 joules = PE + PE                \because\ equation(1)

PE = \frac{400}{2} = 200   joules

mgh = 200

h = \frac{200}{mg}

Substitute the known values in the above equation

h = \frac{200}{2 * 10}

h = 10   

Therefore, height of the stone h = 10 m

b)  

Just before impact, all of the PE in the stone is transformed to KE.