Rotating U tube

Classical Mechanics Level 1

A U-tube is filled with water to height $h,$ as shown. Then the U-tube is spun at a constant rate about arm B.

What will happen to the water level in arm A?

The level will fall The level will rise The level will remain the same

8 solutions

Kelvin Hong
Nov 22, 2017

Consider centrifugal force, the force act on the horizontal water tube and of Arm A, but horizontal one makes more effect.

The centrifugal force will makes the horizontal water tube go opposite side from Arm B which rise the water level in Arm A.

Moderator note:

The centripetal force is a real force that causes something to move in a circle. As one example, the force that a rope exerts upon a ball that's swung in a circle is a centripetal force.

Centrifugal "force" is the apparent force that seems to be operating in a rotating reference frame. For example, if I try to stand on a merry-go-round (without securing myself), it seems there's a force pushing me toward the outside. In reality, my body simply wants to continue linear motion (since there's no force acting on it), so it seems like I'm being pushed off course. But when viewed from above, it's clear that I'm really just moving in a straight line.

In any case, the centripetal force is real and centrifugal is perceived. In this problem, once the apparatus is spinning, the water in Arm A and in the flat bottom needs to be acted on by a centripetal force to keep spinning in a circle. Part of this is provided by the pressure due to the water column in Arm B, which keeps both the water in the flat bottom and the water in Arm A from moving further out on the circle.

In turn, the water in Arm B feels a centripetal force from the walls which keeps it in place.

How about centripetal force? Will it affect the result?

Tristan Chaang - 3 years, 6 months ago

The centripetal force is a real force that causes something to move in a circle. As one example, the force that a rope exerts upon a ball that's swung in a circle is a centripetal force.

In turn, the water in Arm B feels a centripetal force from the walls which keeps it in place.

Josh Silverman Staff - 3 years, 6 months ago

Ah ok, thanks for the explanation!

Tristan Chaang - 3 years, 6 months ago

I would appreciate it if You could explain what You mean when You say that the pressure provided by the water column in Arm B "keeps both the water in the flat bottom and the water in Arm A from moving further out on the circle."

If the (unsecured) water level in Arm A is rising, and what we are able to determine to be the immediate result by way of observation is the centrifugal force which is apparent to us to act on the water, which occurs as a result of the centripetal force exerted on Arm B, would the water's motion not be similar to a human body sliding off of a Merry-Go-Round? As such, "moving further out" on the "circle"?

Thanks in advance, please tag me in reply if that's possible, I appreciate the help!

Trenton Benard - 3 years, 5 months ago

I didn't really know how to do this so I kind of guessed. I think guess and check works best. Maybe next time I should have remembered the centrifugal force and used logical reasoning. I think I would rate this problem an 8 because it was pretty hard. I think I was able to persevere without giving up too quickly because I got to a conclusion.

Lucia Tiberio - 3 years, 6 months ago

Do you feel like you understand what's going on now?

Josh Silverman Staff - 3 years, 6 months ago

Doesn't the speed at which it is spun affect whether or not the water rises?

Hamadi Henderson - 3 years, 6 months ago

I think it will only rises.

Kelvin Hong - 3 years, 6 months ago

The Force in Arm B should be higher, than in A. So the water in B rises faster, to equal the pressure the water in a will sink. Why not?

Niclas Schwalbe - 3 years, 6 months ago

@Niclas Schwalbe – Because the water all have same angular velocity, the centripetal force $F = mr\omega ^2$ which states that Force is proportional to radius, in case mass and angular velocity remain constant, so Arm A received more force than B.

Kelvin Hong - 3 years, 5 months ago

@Kelvin Hong – Thanks for your explanation!

Niclas Schwalbe - 3 years, 5 months ago

I didnt understand your english. Nor the image didnt help understand your question. I thout you mean to spin water in B. Like tea with spoon...

Cinewy Neptune - 3 years, 6 months ago

It was the whole U-tube spinning...

Kelvin Hong - 3 years, 5 months ago

Hi challenge master, it is a common misconception that centrifugal force is fictious. There are some forces that can be made to disappear by changing the frame of reference, but this is not one of them.

It is relatively simple to see this if you consider a ball on a string being swung in a circle. There is a tension in the string, and this tension muat be balanced by a force in the opposite direction if the ball is to maintain an approximately constant radius (simple conservation). That force is the centrifugal force.

Andrew Princep - 3 years, 5 months ago

Md Zuhair
Nov 22, 2017

The level in arm A will rise by $h=\dfrac{\omega^2 d^2}{2g}$ where d is the distance of the limbs from each other

Please explain the reason why the level of water in arm A will rise? This will help others to understand your solution better.

Rohit Gupta - 3 years, 6 months ago

mgh=1/2 (w d)^2

gavin li - 3 years, 6 months ago

The Force in Arm B should be higher, than in A. So the water in B rises faster, to equal the pressure the water in a will sink. Why not?

Niclas Schwalbe - 3 years, 6 months ago

Saif Hassan
Dec 5, 2017

here, for centrifugal force the water will want to go from B to A portion. so water level of A will rise.

Alan Falloon
Dec 8, 2017

Say the water and arm are moving in some direction, now, as the arm curves around and starts to change direction, the water still has moment in it's initial direction and wants to keep going that way. The difference in angle of the tube and the direction of the waters momentum pushes the water to the outside of the U-tube.

Adrian Bacon
Dec 10, 2017

Centripetal, centrifugal; I forget tbh...either way, it acts perpendicularly to the applied force (circular horizontal) ---> ( translational vertical)..therefore downward force on point B + incompressible liquid = upward force at point A. (Side Note: neither translational nor incompressible are real words, but they totally should be because they make complete sense in this context - Physics >>> English ) [ and plz tell me if this justification is wrong/doesn't make sense b/c I'm 2/3 intoxicated & just beep boop bopping around rando math/physics sites for the lelz ]

Richard Cabrejas
Dec 9, 2017

The way I took to understand is: since Einstein proved there can't be a difference between an acceleration and gravity (and gravity is responsible for an equal level in a steady position), a centripetal acceleration will affect the sistem as a slight tilt to the left, rising the level of the liquid in arm A.

Janesh G
Dec 9, 2017

The force required for the rotation acts as centripetal force due to inter atomical force of attraction, inter molecular force of attraction, and other attractive forces keeps the material together but when arm b is considered as axis and the apparatus is rotated in a circular manner , the centrifugal force acting the tops are left free so the water level in arm 2 increases

Any doubts

Janesh G - 3 years, 6 months ago

Any has doubts

Janesh G - 3 years, 6 months ago

Shreyas Belwalkar
Dec 6, 2017

Initially, the pressure of water is same in both the arms. As we start spinning the arm B, it results in an increased pressure on its bottom, which in turn pushes the water in the other arm upwards, as it experiences more pressure due to the pressure on the other arm. Hence the water level in arm A increases

Why would spinning increase the pressure on the bottom?

Josh Silverman Staff - 3 years, 6 months ago

Alan Falloon - 3 years, 6 months ago

Rotating U tube

8 solutions

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