Consider a lift (or an elevator, as Americans call it) with a block inside it. The lift is accelerating upwards, and we are looking at this system from the ground frame.
Wouldn't the net acceleration of the block be $(g-a)$? This is because gravity is pulling the block downwards, but the lift's acceleration is moving it upwards.
Similarly, when the lift accelerates downwards, the block should experience an acceleration of $(g+a)$, but it is exactly the opposite, in both cases. Why is this so?
Best Answer
In standard Newtonian physics the acceleration of the lift is just $\vec a$. There are two forces acting on the block. One is gravity $m\vec g$ and the other is the normal force $\vec N$.
Newton’s 2nd law says that the sum of the forces is the mass times the acceleration so $$\vec N + m\vec g=m\vec a$$
This is the vector expression regardless of if the lift is accelerating up or down. You can then look at the vertical component of this vector equation to solve it. Only then does the sign of the vertical component of $\vec g$ and $\vec a$ come in.