the magnitude of the normal force is greater than the magnitude of the weight of the person
Explanation:
As the elevator moves down, there are two forces acting on the person:
- The weight of the person, [tex]W=mg[/tex], where m is the mass of the person and g the acceleration due to gravity, acting downward
- The normal reaction exerted by the floor of the lift on the person, N, acting upward
This means that Newton's second law can be written as
[tex]\sum F = N-W= ma[/tex] (1)
where we chose upward as positive direction, and a is the acceleration of the elevator.
Here we know that the elevator is moving downward and it is slowing down: this means that the velocity is negative (upward), and the acceleration is in the opposite direction (upward), so the acceleration is positive.
Eq.(1) can be rewritten as
[tex]N=W+ma[/tex]
and as we said that [tex]a>0[/tex], this means that
[tex]N>W[/tex]
So the magnitude of the normal force is greater than the magnitude of the weight of the person.
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