Elevators... :(

[MedPR]

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I guess I have really bad intuition when it comes to elevators and accelerating upward/downward.

A scientist operating a pendulum in an elevator sees that the pendulum's period is shorter than can be accounted for by gravity alone if she takes measurements when the pendulum apparatus is moving with a constant:

C. downward acceleration
D. upward acceleration

The relevant equation, if you don't know it, is Period = 2pi sqrtL/g

The answer is D because: When an elevator accelerates upward, you feel as if gravity is pulling you down harder. The same effect will make the pendulum "feel" as if gravity is pulling on it harder. This will decrease the period.

So my intuition (obviously wrong) was/is that when you are accelerating downward in an elevator, that you are adding to the already downward acceleration due to gravity (like if a car is rolling down a hill and you rear-end it with your car.. It is now accelerating downhill even faster). Why isn't that correct? Why is your downward acceleration greater when you are accelerating upward in an elevator?

 

[Ssina]

elevator is not really pulling you down, it is slowing you down from free falling.... so it is only applying a little bit of force to decrease the acceleration downwards, supplied the gravity so we don't go into a free fall... vs. going up, then the elevator has to not only pull you up against the gravity, but it have to supply a little bit more force than mg to acceleration upwards (so it can go up and eventually reach a constant velocity after it's started

when rear ended then the other car pushes the first car down the hill with the gravity, so it's gravity plus that force in the same direction.

 

[dmf2682]

elevator is not really pulling you down, it is slowing you down from free falling.... so it is only applying a little bit of force to decrease the acceleration downwards, supplied the gravity so we don't go into a free fall... vs. going up, then the elevator has to not only pull you up against the gravity, but it have to supply a little bit more force than mg to acceleration upwards (so it can go up and eventually reach a constant velocity after it's started

when rear ended then the other car pushes the first car down the hill with the gravity, so it's gravity plus that force in the same direction.

this. You know that sensation your stomach makes when the elevator starts moving downwards? that's your downward acceleration being suddenly decreased. What you feel as "gravity" has decreased. Conversely when the elevator starts moving upwards "gravity" as you feel it has increased (i.e. you're heavier).

 

[JD7]

If the elevator was "pushing" you down then your body would have to be in contact with the roof of the elevator.

You body feels the effect of inertia when the elevator is going down or up. Also if the elevator is going down at the acceleration of gravity then you would be flying in the elevator, and when it is still it is actually doing 1g force on you due to the normal force. Gravity = -Elevator force (no net movement yet both the elevator and gravity are doing force).

 

[Meredith92]

Hey so I have this same question again... I did it more mathematically but it still doesnt make sense to me.

Basically we want to see how the value for "g" changes with upward vs. downward acceleration in an elevator

upward acceleration:
Fn-mg=ma
-mg=ma-Fn
mg= Fn-ma

downward acceleration:
-ma=Fn-mg
-ma-Fn=mg
ma +Fn=mg

so in comparing values of g, it seems as though g is GREATEST when there is a downward acceleration.

However, the answer seems to be solving for normal force, not g. It says we should think about how the pendulum "feels" gravity... Why are they comparing the normal forces/ weight? The question specifically asks about g??



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Just found this awesome explanation by milski

milski
10-24-2012, 06:18 PM
You cannot increase gravity - it is a constant, at least at small distances from Earth. What the previous two posters said should be fairly helpful. If you want to approach the problem in a more formal way, you have to consider that the g in the formula for the period is related to the tension of the string, so a way to "increase g" is to increase the tension in the string and the way to do that is by a force applied upward, which means an acceleration upward. That's still only an estimation but the exact derivation of what the motion will be gets too complicated.

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so i guess that means even though there is a "g" in the period equation, we care more about what is perceived by the pendulum... this is still very strange conceptually for me, because how does a pendulum "feel" weight?? i guess through the tension which affects period.. its just weird because the tension force is not in the equation for period..

 

[milski]

G is acceleration - increasing g means that you are accelerating faster downwards, the same direction in which gravity accelerates you. 😉

The normal is the 3rd law opposite force of the weight - if it's smaller, you feel lighter to the floor. Your internal organs act line floors to what's above them, making you feel lighter yourself.

The pendulum "feels" gravity as the force, which pulls it back toward its equilibrium point. The tension is a 3rd opposite to a component of gravity, so in a way you can include it too.

 

[Meredith92]

To be honest I still don't totally understand it because the force that brings the pendulum back to equil is mgsin(theta) and if the value for g doesn't change I don't understand how the force or period ( which also doesn't include tension/force) changes.

I understand what you're saying in terms of a person in an elevator / normal force but I still am confused about how it can affect a pendulum.

Thanks again for all your great help

 

[JaBoomDay]

I never understood these elevator questions until I watched the Kahn Academy physics videos. I highly recommend them.

 

[Meredith92]

Oh wait I think I may get it- If tension/ normal force is less in upward motion that means when solving for the resultant vector of tension and gravity, mg now has more of an effect! That makes it move more quickly to equilibrium!!
Got it!! Thanks milski!

 

[milski]

The force which brings it back is m.sinθ.g, where g is the acceleration. In the elevator, the acceleration of the system is not just g but it has added whatever the acceleration of the elevator is. While g itself will not change, you'll have something like m.sinθ.(g+a) in your formula in that case.

It may feel that I'm contradicting myself - sorry, if that's the case. The summary is that g, the acceleration due to Earth's gravity does not change but the system in the elevator experiences a different acceleration, g+a.

 

[Meredith92]

The way I learned to deal w these problems was working with forces... ma, mg, Fn... And see how the direction of "a" affects the Fn or weight.. I don't see mathematically how you've an just add together g and a...
If at all possible could you show those steps?

 

[milski]

If you can see how "weight" is affected, would you agree that the weight of the pendulum is m(g+a) too?

From the formulas that you have written below:
Fn-mg=ma or Fn=ma+mg=m(a+g)

You might be taking my previous post slightly out of context. While g itself will not change, the value that we use in place of g when considering the elevator system will change.

Wait, I think I am getting what bothers you - how does the pendulum "know" that a+g needs to be used when it only "feels" g gravity?

When you derive the equation for the period, you use the fact that the attachment point of the pendulum is stationary and the pendulum swings follow a part of a circle. If you were to derive the same equation for a pendulum on an elevator, you'll have to describe the attachment point accelerating up/down and the trajectory of the pendulum being something much more complicated - oscillations left/right as it accelerates up/down. Solving that will get you the result that the period is the same as if you were using g+a instead of g in the stationary formula.

What makes the solution different is the fact that the pendulum stays at a fixed distance from the accelerating attachment point and the way that is transferred to the pendulum is through the tension of the string.

 

[Meredith92]

ahhhh thank you!!! That completely makes sense now! I really appreciate you taking the time to explain it/ figure out what was confusing me!

 

[milski]

ahhhh thank you!!! That completely makes sense now!

👍👍

 

[MedPR]

This still doesn't make sense to me. Good thing it doesn't matter anymore. 👍

 

[gettheleadout]

This still doesn't make sense to me. Good thing it doesn't matter anymore. 👍

Wait till your patient has orthostatic hypotension and you're both trapped in a constantly accelerating elevator.

 

[milski]

Wait till your patient has orthostatic hypotension and you're both trapped in a constantly accelerating elevator.

Speed IV? One patient, one elevator, one doctor...