Let’s have a 60-kg elevator man stand on a weighing scale in a stationary elevator. For ease of discussion, we will take g to be 10 m s-2.
This means the Earth pulls the man downward with a gravitational pull of . The man in turn pushes the weighing scale downward with a normal contact force of . The weighing scale “feels” this 600 N force, and displays a reading of 60 kg.
Now take a look at the following statements.
A: The weight of the man is 600 N. (mg)
B: The man’s weight of 600 N acts on the weighing scale. (N’)
C: The man weighs 60 kg. (m)
Do you realize that when somebody says “weight”, he could be referring to mg, N’ or even m? But m is the mass of the man, mg is the gravitational force that Earth exerts on the man, and N’ is the normal contract force that the man exerts on the weighing scale. Each of them is a different quantity – m is not even a force, and mg and N’ are not even of the same magnitude (when the elevator is accelerating).
I suspect that even among scientists, “weight” means different things to different people at different times. Personally and secretly, I prefer N’ to be called the weight (because N’ is the “weight” in statements such as “the astronaut is weightless”, “the weight of the man caused the chair to collapse”, “shift your weight more to your left foot”, etc), and for mg to be referred to simply as the gravitational pull. But then, I can see the convenience of calling mg weight instead of gravitational pull; it is one syllable versus six syllables.
So what is Cambridge’s stand on this? Under the H2 syllabus: mg is called the weight, N’ (or N) is called the normal contact force, and m is called the mass. In some situations, mg will be referred as the true weight, in contrast to N’ (or N) which is called the apparent weight. Since you are taking the Cambridge H2 examinations, you should stick to the official Cambridge terminology. Having said that, I feel that we should live with the ambiguity. When we hear or read the word “weight”, we should just figure out which “weight” is being referred to base on the context. 😊