As a new physics teacher, I was explaining how to find the weight of an object sitting on a table near the surface of the Earth. It bothered me when a student asked, “The object is not accelerating so why do you multiply the mass of the object by the acceleration due to gravity?” I answered something like, “That's true, but if the table were not there, the object would accelerate at that rate.” The really determined students might go on to ask, “Yes, but what if the object were already sitting on the surface of the Earth?” About that time, I would hope the bell would ring so that this whole discussion could be delayed until the next day. The next day, I would explain that the newton unit is the same as a kg-m/s2, so multiplying the mass in kilograms times the acceleration due to gravity would give an answer in newtons. It all made sense to me, but I am sure that the students just went along with me to get the right answer.
REFERENCES
I call this “Four-Step Analysis.” See p. 72 in Teaching about Kinematics, an AAPT/PTRA Teacher Resource.
Since both slope and mass are symbolized by “m,” a capital M is used in this case for mass.
There is a small difference between gravitational force and weight due to the orbital and rotational motions of the Earth. This is often not discussed until later.