Vectors and Forces

Newton's Third Law

equal and opposite

When one object pushes another, the second pushes back just as hard in the opposite direction.

Example

Whenever one object pushes another, the second pushes back just as hard in the opposite direction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two blocks in contact

Block A pushes on block B. Newton's third law says B pushes back on A just as hard, in the opposite direction.

FA→B=− FB→AF_{A \to B} = -\,F_{B \to A}
Block A pushes block BTwo touching blocks with one arrow from A pushing B to the right.ABA on B

Equal in size, opposite in direction

If A pushes B with 6 newtons to the right, then B pushes A with 6 newtons to the left. The two arrows are the same length, pointing opposite ways.

FA→B=6 N,FB→A=6 N (opposite)F_{A \to B} = \hl{6}\ \text{N},\quad F_{B \to A} = 6\ \text{N (opposite)}
Equal and opposite pushesTwo touching blocks: block A pushes block B to the right, and block B pushes block A to the left with an arrow of the same length.ABA on BB on A

The pair stays equal at every size

Try smaller and larger contact pushes. Each row has equal sizes on the two different blocks; the pair does not cancel on one block because the forces act on different objects.

FA→BFB→Asize difference2 N2 N0 N4 N4 N0 N6 N6 N0 N\begin{array}{c|c|c}F_{A \to B} & F_{B \to A} & \text{size difference} \\ \hline 2\ \text{N} & 2\ \text{N} & 0\ \text{N} \\ 4\ \text{N} & 4\ \text{N} & 0\ \text{N} \\ 6\ \text{N} & 6\ \text{N} & 0\ \text{N}\end{array}
mechanics One 6 N push and its equal-and-opposite partner make the action-reaction pair concrete.