Newton's Third Law — Question 1

Question 1

The reaction to weight acts on Earth

A book rests on a table. Earth pulls the book downward with 10 N; the table pushes it upward with 10 N.

1. Identify the third-law partner of Earth’s force on the book.

2. Identify the partner of the table’s force on the book.

3. Why are the two stated forces on the book not a third-law pair?

Question 1 - Solution

The reaction to weight acts on Earth

(a) Reverse agent and recipient for gravity.

$$\vec F_{B\to E}=-\vec F_{E\to B}\ \Rightarrow\ \boxed{\vec F_{B\to E}=+10\hat y\,\mathrm N}$$ The book pulls Earth upward toward the book with 10 N. The two gravitational forces belong to the same book-Earth interaction.

(b) Reverse the contact interaction.

$$\vec F_{B\to T}=-\vec F_{T\to B}=-10\hat y\,\mathrm N$$ The book pushes the table downward with 10 N. That is the partner of the table’s upward force on the book.

(c) Compare the bodies acted upon.

$$\vec F_{E\to B}+\vec F_{T\to B}=\vec0\quad\text{(both recipients are B)}$$ The two given forces both act on the book and come from different agents. They balance here because the book has zero acceleration. A third-law pair always acts on different recipients and exists even when either recipient accelerates.