If you are standing on a scale in an elevator, what exactly does the scale measure

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A person who normally weighs 700N is riding in an elevator that is moving downward but slowing down at a steady rate. If this person is standing on a bathroom scale inside the elevator, what would the scale read? Please give an explanation.

The weight indicated on the scale will only increase as long as the elevator accelerates you upwards. For most of the ride, when speed is constant, the indicated weight will be the same as in the static case, and at the end, when the elevator decelerates, the indicated weight will decrease.

The weight force is composed of two parts:

• Weight due to gravity ($W_g = m\cdot g$)
• Weight due to vertical acceleration ($W_a = m\cdot a$)

What the scale will indicate is the sum of both: $W = W_g + W_a$

If you integrate the weight indication over time and compute the average after the elevator has stopped, you will find that it will exactly be your static weight.

Also, on the way down, the indicated weight will only be lower as long as the elevator accelerates downwards, and towards the end of the ride, when it decelerates again, you will see your indicated weight increase. It is the same as on the way up, only in reverse because now the acceleration will work in the opposite direction.

If the person was not moving, the scale would read #539N ["down"]#:

#F_"g"=mg#

#=55(9.8)#

#=539#

If the elevator is moving up, we can't say for sure what the number would read. What we do know is that the number would be greater than #539#.

I'll explain.

As we all know, mass is not weight. The difference is that weight includes the force of gravity, while mass is used to define how much matter your make up.

When you stand on a scale, the scale measures your force of gravity AKA weight. This measurement is influenced by Earth's gravitational force of #9.8N "[down]#.

However, in certain situations the force of gravity is equal to the net force: #F_"g"=F_"NET"#. This is because #mg=ma#.
=> Where #m# is the mass of the object.
=> Where #g# is the gravitational force; NOT FORCE OF GRAVITY
=> Where #a# is the acceleration of the object.

Both #a# and #g# have a value of #9.8#, the unit varies between #m/s^2# and #N# respectively.

If you are on an elevator (on Earth), your mass is constant.

However, if the elevator is moving (and you're on a scale), you'll notice that your weight changes depending on where the elevator is moving.

The only possible factor that can explain this change is the acceleration of the object - you.

When the elevator (you) moves up - acceleration increases (adding on to the #9.8 m/s^2#) and there is more normal force applied to the floor. This results in a larger number on the scale.

Consequently, when the elevator (you) moves down - acceleration decreases (subtracting from #9.8 m/s^2#), there is less normal force applied to the floor, resulting in a smaller number on the scale.

Keep in mind that your mass is not changing, it's the influence of your acceleration.

This relationship is beautifully illustrated in this image:

As you can see, when the elevator moves up, the weight of the fish increases.

When the elevator moves down, the fish's weight decreases.

The fish did not undergo a change to its physical body - matter was removed/gained. Only its acceleration, which ultimately changed the #F_"g"# - its weight.

Hope this helps :)

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