If a person in the elevator were standing on a bathroom scale calibrated in newtons, what would the scale read while the elevator was (a) descending at constant speed and (b) while slowing to a stop? Please explain your answers.
The person is standing on a bathroom scale in an elevator. The bathroom scale is calibrated in newtons. This shows that the reading on the scale is the weight of the person. If the person's mass is M kg, the reading in the scale is F = M*a where a is the acceleration of the person and F is the resulting force applied on the scale.
When the elevator is descending at constant speed there is no force applied on the person and the net acceleration is zero. As a result the force exerted on the scale is M*0 = 0 N.
When the accelerator slows down there is a decrease in its velocity in the downward direction. Due to inertia the person continues to move downwards at the constant velocity that the elevator was moving at earlier. As the elevator has to come to a stop a force is exerted on the person in the upward direction which results in a counterforce applied by the person on the scale in the opposite direction. This is equal to M*a where a is the acceleration of the elevator. The scale shows a positive reading when this happens.
I assume this question relates to the common example of the equvalence priciple of general relativity. The idea is that if you are in a non-inertial frame (i.e. accelerating) then it would be equivalent to being in a gravitational field of the same acceleration, so if you were in an elevator outside of any gravitational field that was being pulled UPWARD at an acceleration equal to that due to gravity on Earth, then it would feel as though you were on Earth. To answer yor question:
I assume you mean an elevator outside of any gravitational field.
(a) If you are moving at constant speed in any direction, then you are in an inertial frame, which would be equivalent to zero gravity so the scale would read zero.
(b) Slowing to a stop from your downward motion is an upward acceleration, so this time it is the same as being in a gravity field. The scale would read the force that your body exerts on the scale, which according to Newton's second law is F=ma, the product of your mass and the acceleration of the elevator.
It's interesting to note that because both you and the scale have mass, they produce their own gravitational field and so will always attract each other, but this force is exceedingly weak and would be unnoticable.
Hope this helps.