Question

How does F=ma (Newton's second law) combine into ma=F-mg?

Answer 1

For this equation, F = ma

F = net force on the body ,

m = mass of the body

a = acceleration

Now, for the equation : ma = F - mg

F here denotes the applied external force

ma = net force on the body

mg = force on the body due to gravity

As the applied external force is opposite to the force of gravity (acting downwards), the net force will be directed towards up and the net force is given by the vector sum of the two forces acting on the body (F and mg)

Now, as the two forces are opposite to each other, the net force = ma = F - mg