How is weight measured in an accelerating elevator?

In summary, the balance reads the apparent weight of an object, which is the force needed to balance the weight of the object. When in an accelerating elevator, the scale will read a different apparent weight due to the additional inertial forces caused by the elevator's acceleration. However, the scale is only measuring the normal reaction force from the ground and does not take into account the net force on the object. This is why the scale may not match our perception of weight in certain situations, such as free fall.
  • #1
ProPM
66
0
Hi,

I'm a bit confused:

Picture an elevator accelerating upwards with a person standing inside on top of a balance. Since the elevator is accelerating upwards, the Normal reaction force from the ground must be greater than the weight of the person.

My question is: Why doesn't the scale on the balance read the net force? In the end, the balance is experiencing the force of weight of the person downwards and the force upwards from the ground. Why does it read the full normal reaction force? Or why do we also don't experience only the net force since we have a force pushing us down and one pushing us up?

Sorry, I hope I made what I mean clear.

Thanks,
Pro PM.
 
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  • #2
ProPM said:
Hi, Why doesn't the scale on the balance read the net force? In the end, the balance is experiencing the force of weight of the person downwards and the force upwards from the ground. Why does it read the full normal reaction force? Or why do we also don't experience only the net force since we have a force pushing us down and one pushing us up?

Keep in mind that a balance reads what he manufacturer calibrated it to read. When I step on the scale in my bedroom, it reads the force with which it pushes up on me (which you called "the full reaction force"). By the third law of motion, that force is equal in magnitude to my weight. In a sense, the balance reads that because I want to use it to find my weight.

(Note that this is consistent with a balance reading my weight as zero in free fall.)

In the situation you describe, the balance would have to read the upward force of the elevator on it if the person were not on it. When the person steps on, the reading goes up, even though the net force on the scale decreases.

Does that address your question?
 
  • #3
Hi :smile:

So, if a scale were to read the upward force the elevator was exerting on it, it would not measure my weight? Because the forces are in opposite directions - they are programmed to measure two different things?

Another quick doubt that arose: If I were under free fall and I touched a the balance while falling, the normal force due to contact would not give me any sensation of weight.

And, what's confusing me most, despite the fact I know I'm wrong, I just have a hard time making myself understand :cry: is because I keep thinking: How can my weight sensation be only the upward force is I have a downward force acting one me too! I picture a vector diagram of myself in the elevator showing the resultant force being upward and that I should only feel that force for some reason...
 
  • #4
A *balance* compares the forces on two objects (think of the archetypical equal-arm balance). In an elevator, both objects will experience the same accelerations and thus the inertial forces will remain in balance.

A spring scale, on the other hand, employs a spring with a given spring constant. It's readings are sensitive to the net force felt by the object being weighed, and accurate scales must be calibrated for the local value of 'g'.
 
  • #5
I found a better way to express my doubt: If the elevator is accelerating upwards the spring scale will read: The normal reaction force of my true weight + the upward force from the elevator ground?

Thus: 100 kg man, a = 2m/s^2

N - mg = ma
N - 1000 = 200
N = 1200

That is, 200 N force from the elevator ground?

But, then that same logic wouldn't make sense for when the elevator is accelerating downwards: The upward force would still be greater than the downward force.

Don't get me wrong, I understand why we feel lighter and heavier while in a lift but the scale is killing me!
 
Last edited:
  • #6
Think in terms of the net acceleration. g is an acceleration. The elevator is providing another acceleration acting along the same axis as g. If the elevator is accelerating upwards, then it adds to g (inertial forces generated by its action will act downwards). If the elevator is accelerating downwards, it subtracts from g. The result is a new net acceleration, call it g', that will act on an object contacting the elevator floor.

For your example, and taking g to be 10 m/s2, if the elevator is accelerating upwards at 2m/s2, then the 'weight' of the man on the elevator floor is

(10 + 2)m/s2 * 100kg = 1200N

If the elevator is accelerating downwards,

(10 - 2)m/s2 * 100kg = 800N
 
  • #7
Cool! Thanks!
 
  • #8
ProPM said:
So, if a scale were to read the upward force the elevator was exerting on it, it would not measure my weight? Because the forces are in opposite directions - they are programmed to measure two different things?

Your questions sent me to my intro college text by Tipler. After defining weight as the force of gravity acting on a body, he wrote "The scale is calibrated to read the force it must exert (by the compression of springs) to balance our weight. The force which balances our weight is call our apparent weight."

Think through what it would be like if a scale were designed to read the upward force acting on it. Suppose it has a mass of 2 kg. We would have to change the display to read 19.8 N when the scale sat at rest (or moved uniformly). If the scale is in an elevator that experts an upward force of 4.2 N, the scale will now read 25 N (while the net force on it is 19.8 N down + 4.2 N up = 15.6 N down).

Not a very useful scale.

Another quick doubt that arose: If I were under free fall and I touched a the balance while falling, the normal force due to contact would not give me any sensation of weight.

Correct, and the scale would read zero. That why we say you are weightless in freefall (including in orbit).

And, what's confusing me most, despite the fact I know I'm wrong, I just have a hard time making myself understand :cry: is because I keep thinking: How can my weight sensation be only the upward force is I have a downward force acting one me too! I picture a vector diagram of myself in the elevator showing the resultant force being upward and that I should only feel that force for some reason...

I understand. I recall wrestling with that myself, and see my students doing the same. As I see it, the discomfort comes from mixing the view of Newtonian physics with the way you grew up thinking the world works. I suspect it is related to the conflict between thinking a passenger is thrown rightward into the door of a left-turning car (rather than the roadside observer’s view that the car door pushes the passenger leftward).

I find comfort in sticking to what the laws tell me is unambiguously true. Gravity pulls the guy in the elevator down, the elevator pushes the guy up. He accelerates in the direction of the net force. What the scale says doesn’t come into play.
 
  • #9
Oh Man! In that whole discussion I was thinking that "balance" was just a regional term for scale. It's been so long since I've used a two pan balance that it didn't occur to me to interpret it that way.
 
  • #10
First of all, thanks both of you, for taking the time. And sorry, I did mean scale from the beginning :redface:
 
  • #11
any advice? showthread.php?t=612910
 

1. How does an elevator accelerate upwards?

An elevator accelerates upwards by using a motor to pull cables that are attached to the elevator car. The motor creates a force that pulls the elevator car up, causing it to accelerate.

2. How fast does an elevator accelerate upwards?

The acceleration speed of an elevator can vary, but it typically ranges from 0.3 meters per second squared to 1.0 meter per second squared. This means that the elevator increases its speed by 0.3 to 1.0 meters per second every second.

3. Is it safe to accelerate upwards in an elevator?

Yes, it is safe for an elevator to accelerate upwards. Elevators are designed and built with safety features to ensure a smooth and controlled acceleration. The cables and motor are also regularly inspected and maintained to ensure safe operation.

4. What factors can affect the acceleration of an elevator upwards?

There are several factors that can affect the acceleration of an elevator upwards. These include the weight of the elevator car and its occupants, the power and efficiency of the motor, and any external forces such as wind or air resistance.

5. How does the acceleration of an elevator affect the sensation of movement?

The acceleration of an elevator can affect the sensation of movement, as a faster acceleration can make the ride feel more intense or jerky. However, modern elevators are designed to have a smooth and gradual acceleration, minimizing any discomfort or noticeable movement for passengers.

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