Show that the units for g, the acceleration due to gravity, can be written as N / kg?
Actually, it is misleading to think of it as “acceleration due to gravity”. It is not necessarily an acceleration, except when no other forces come in to play. Especially in situations like the yo-yo or Atwood’s machine, “acceleration due to gravity” is a misleading term, since it accelerates due to gravity as an energy source, but it is hindered by inertia of other directions of motion. It is better called gravitational field strength, as in gravitational force per unit mass. By definition of the units for force and mass, it is obvious that gravitational field strength has units Newtons/kilogram. When no other forces come in to play, the net force is m*g downward, and Newton’s second law Fnet=m*a sets m*g = m*a, and g=a. Knowing that Newtons dissect as kg-m/s^2, Newtons per kilogram dissect as m/s^2.
