Question

A box of mass M sits on the floor of an elevator at rest. Gravity (which has a strength set by the local acceleration due to gravity g) pulls the box and the floor pushes the box. The net or total force on the box is zero.

What is the force on the box from the floor? Give both the magnitude and the direction.

Now imagine that the elevator is accelerating upwards at acceleration a. Now the two forces on the box don’t balance! Because, after all, the box is accelerating upwards. What is the force on the box from the floor in this case?

Now imagine that the elevator is accelerating downwards at accelerationa. Same question.

Now imagine that the elevator is accelerating downwards at accelerationa = g. Same question. Look up the “vomit comet” and tell me what this problem has to do with that airplane.

Answer 1

When the box is resting on floor, forces acting on the box are , i) Gravitational force vertically down (ii) Normal force vertically up

Net force acting on the box is

Force on the box from the floor is , direction is upwards.

Now elevator is accelerating upwards with acceleration .

Net force acting on the box is

Force on the box from the floor is , direction is upwards.

Now elevator is accelerating downwards with acceleration .

Net force acting on the box is

Force on the box from the floor is , direction is upwards.

Now elevator is accelerating downwards with acceleration .

Net force acting on the box is

Force on the box from the floor is , no direction.

The above is just the case of "vomit comet" , where the box feels weightlessness when placed in a free falling airplane.