Newton's Third Law — Question 10

Question 10

A mutual-force claim must reverse both bodies and direction

A report lists A on B as +7 N, B on A as -5 N, B on C as -4 N and C on B as +4 N along a shared axis. All refer to the same instant.

1. Which pair violates the third-law condition?

2. If A on B is trusted, repair B on A.

3. Can adding an external force to A repair the incorrect pair entry without changing that entry?

Question 10 - Solution

A mutual-force claim must reverse both bodies and direction

(a) Check each interaction separately.

$$F_{A\to B}+F_{B\to A}=7-5=2\,\mathrm N\ne0,\quad F_{B\to C}+F_{C\to B}=-4+4=0$$ The A-B entries sum to +2 N and are inconsistent. The B-C entries are equal and opposite and pass.

(b) Reverse the trusted force.

$$\boxed{F_{B\to A}=-F_{A\to B}=-7\,\mathrm N}$$ B on A must be -7 N.

(c) Distinguish mutual and total forces.

$$F_{{\mathrm{net}},A}=F_{B\to A}+F_{{\mathrm{ext}},A},\quad F_{B\to A}\equiv-F_{A\to B}$$ No. An external force changes A’s net force but does not alter the required partner of the specified A-on-B force. Confusing a total-force entry with an individual interaction could explain the report, but it would require relabeling or correcting the data.