Mass and Newton's Second Law?

Question

While trying to understand the second law of Newton from _"An Introduction to Mechanics"_ by Kleppner and Kolenkow, I came across the following lines that I don't understand: > "It is natural to assume that for three-dimensional motion, force, like acceleration, behaves like a vector. Although this turns out to be the case, it is not obviously true. For instance, if mass were different in different directions, acceleration would not be parallel to force and force and acceleration could not be related by a simple vector equation. Although the concept of mass having different values in different directions might sound absurd, it is not impossible. In fact, physicists have carried out very sensitive tests on this hypothesis, without finding any variation. So, we can treat mass as a scalar, i.e. a simple number, and write $\\vec{F} = m\\vec{a}$." The lines above lead me to question: 1. Why is it not" obviously true" that force behaves like a vector? 2. Why is it not impossible for mass values to be different in different directions?

Answer 1

From your citation:

"Although the concept of mass having different values in different directions might sound absurd, it is not impossible. In fact, physicists have carried out very sensitive tests on this hypothesis, without finding any variation."

This does not make sense....the 2nd sentence purports to support the 1st sentence, but then says no variation was found.

I have never heard of mass being anything but a scalar quantity.