Question

When is the sum of forces in the y direction equal to (N - mg) as opposed to (mg - N)? Can you explain what situations in Physics signify each, and moreover, how they relate to the free-body diagrams? Thanks!

Answer 1

We should not get confused with the sign convention along Y direction weather we take upwards as + ve and downwards as -ve or upwards as -ve and downwards as +ve

If upwards is + ve and downwards is -ve then the first equation (N - mg) is used, as N is always directed along upwards for an object lying on a horizontal surface and mg is always directed in vertically downward direction.

If upwards is -ve and downwards is +ve then we can use the senond equation (mg - N), here also N is directed in the up direction which is negative and mg is directed in down direction which is positive.

Hence we should remember that sign convention is very important when applying Newtons 2nd law. Along with N and mg we have assign sign convention for other forces also (if present), as above.