Is Newton's Second Law Valid in an Accelerating Reference Frame?

[briteliner]

Homework Statement

In a lab frame of reference, an observer finds Newtons second law is valid in the form of Fnet=ma. Show that Newtons second law is not valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration a1. assume that mass is an invariant quantity and is constant in time.

Homework Equations

f=ma

The Attempt at a Solution

i don't get how to show this, i get how to show that the velocities and displacement would be different but not how to relate that to the force

 

[edziura]

Suppose instead that we wish to show that NSL is valid in a 2nd frame moving at constant speed b. The Galilean (sp?) transformation is

x' = x - bt

where the primed quantities are in the moving frame, and b is some constant speed. If we differentiate this twice with repsect to time, we obtain

a' = a

Since mass is invariant, F = ma holds in both frames.

Now do the same thing, but assume that b = a₁ t, also the speed of the moving frame but written in terms of a constant acceleration a₁ and time. You should find that acceleration is this case is not invariant.