A book of a mass 0.5kg is dropped from a height of 2.8m. How much mechanical energy does it have right before it hits the ground? (Assume there is no air resistance.) Acceleration due to gravity is g= 9.8 m/s^2.

13.7 J

Explanation:

In absence of air resistance, the mechanical energy of the object is conserved during the fall: this means that the initial gravitational potential energy that it has at the beginning of the fall will be entirely converted into kinetic energy when the book is just about the hit the ground.

Therefore, this also means that we can calculate the mechanical energy at the beginning of the fall, as this will be equal to the mechanical energy just before the book hits the ground.

At the beginning of the fall, the mechanical energy is all gravitational potential energy:

where

m = 0.5 kg is the mass of the book

is the acceleration of gravity

h = 2.8 m is the height above the ground

Substituting,