When a plane is accelerating upwards, why is both the upwards acceleration and gravitational acceleration positive?

Question

At a weight m, a plane is acceleration upwards at rate of a. We also remember the value of g.

From my understanding, we have two opposite forces that we care about.

• The force due the gravitational acceleration, which points in the negative y-direction,
• The force of the upwards acceleration, which points in the positive y-direction.

The first force must be equal to m times g, while the second would be equal to m times a. However, that is not the case with the upwards acceleration.

My physics book gives this reasoning for calculating the upwards force:

I don't understand why we would add g, since it points in the opposite direction?

Answer 1

To accelerate the mass $m$ at constant acceleration $a$, you need to apply a force ($F_{body}$) on the body upwards such that: $$F_{net} = ma$$

Now drawing the forces at play, you get two forces: $F_g=-mg$(downwards) and $F_{body}$(upwards)

They should sum up to $F_{net}$, therefore:

$$F_{net} = F_g + F_{body}$$ $$ma = -mg + F_{body}$$ $$F_{body}=m(a+g) \text{(upwards)}$$

This is the apparent weight you feel.

To make it even more intuitive, consider the example when you step into an elevator and it "just" starts to go up. At that very moment, you suddenly feel that your weight has increased or the ground is pushing onto you!