A person is standing on a scale in a elevator accelerating downward. compare the reading on the scale to the person's true weight.
A) greater than their true weight
B) equal to their true weight
C) less than their true weight
The safe answer is C. See below why it could also be D:
The best way to think of weight is this: weight is the measurement of resistance of a given mass to falling.
On the earth, everything that has mass wants to fall. We call that gravity. When you stand on the ground, the ground prevents you from falling. If you stand on a scale that is on the ground, the gound stops the scale from falling, and the scale stops you from falling. It also measures how much it stops you from falling, and that is called your weight.
Now stand on a scale in an elevator. If the elevator is stationary, then the scale is prevented from falling by the floor of the elevator and the scale prevents you from falling and measures your "true" (at rest) weight. But, if the elevator begins to fall (accelerates downward) and you continue to stand on the scale, you will weigh less and less (as the elevator floor, you and the scale are falling at the same rate) until the whole system is in free fall at which point you, the elevator and the scale will weigh nothing at all.
Of course, if you should hit the ground at some point, you will all weigh a great deal more than you did when you started.
The correct answer here is C. The reading on the scale would be less than the true weight of the person.
If you were standing on the scale while the elevator was at rest, you would weigh your true weight. The scale would be pushing you upward (to keep you from falling) with a force equal to your true weight.
But then the elevator starts taking you downwards -- it's accelerating you downward, along with the scales. So you've got this downward force. At the same time, there's an equal upward force being exerted on you AND the scale.
That upward force is subtracted from the force with which the scale was originally pushing you upward. Therefore the scales pushes you up with less force than it originally did and the reading is lower than your true weight.
The reading shown by the scale is proportional to the force exerted by the person on the scale.
When the scale is has no acceleration in the vertical direction, this force is equal to mass (m) of the person multiplied by acceleration due to gravity (g).
However when the lift is accelerating downwards, part of this total force of gravity is being converted in the kinetic energy of the person standing on the scale, which increases due to the increase in downward speed, as a result of acceleration of the lift. Thus the net force exerted on the scale is reduced, and therefore the reading shown in the scale will be less than the true weight of the person.
Option C) of the given choices is correct.
Since the elevator is accelerating downward with an acceleration a say, the person of mass m has the force acting on him by the elevator say in F in opposite direction. Then the net force on the person is mg-F = ma.
F = mg - ma = m(g-a)., which is mmeasured by the reading of the scale measuring the net down ward force of man. The weight force of him is less by ma than that of his normal weight force.