A history book that weighs 30 N is placed on top of a literature book that weighs 10 N. If up is considered the positive direction, what is the force that
The history book exerts on the literature book?
To determine the force that the history book exerts on the literature book, we need to consider Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
In this scenario, the literature book is supporting the weight of the history book placed on top of it. The weight of an object is the force of gravity acting on it, given by the equation:
Weight = mass × gravitational acceleration
However, since we are only concerned with the force (which is a vector quantity) and not its magnitude, we can simplify the equation using Newton's Second Law of Motion:
Force = mass × acceleration
Assuming that both books are at rest and there is no acceleration, we can equate the forces to determine the force that the history book exerts on the literature book:
Force (history book on literature book) = Force (literature book on history book)
Using the equation:
Force = mass × acceleration
We can rewrite it as:
m₁ × a₁ = m₂ × a₂
Where:
m₁ and m₂ are the masses of the history and literature books, respectively,
a₁ and a₂ are the accelerations of the history and literature books, respectively.
Since both books are at rest, their accelerations are zero. Therefore:
m₁ × 0 = m₂ × 0
This means that the force the history book exerts on the literature book is zero. In other words, there is no additional force acting on the literature book as a result of the history book being placed on top of it.