# Slight rearrangement of Newton's Law

1. May 18, 2015

### Timothy S

Instead of F = ma, is it valid to write λxa = F, (in the case of a linear, one dimensional object). Does this make sense, im just curious. Also, would this lead to any real insights about a system?

Edit: For clarity's sake, I replaced mass with linear density times length, which in this case is in the x direction.

2. May 18, 2015

### Staff: Mentor

Depends on how you use it. It can be meaningful.
As an example issue, does every part of your line have the same acceleration?

3. May 18, 2015

### Philip Wood

One case for which we use the law in more or less this form is for studying the propagation of mechanical waves through a medium such as a spring. We'd consider a small length, $\Delta x$, of the spring, and the resultant, Fres, of the slightly different pulls on each 'end'of this piece of the spring, from neighbouring parts of the spring.

Then $\lambda \Delta x\ a$ = Fres

Fres is then found, essentially by applying Hooke's law, but it's quite tricky as Fres arises because the displacements of particles of the spring from their equilibrium position vary as we go along the spring.