The Secret World of Arrietty

Classical Mechanics Level 2

"Thank you, it's really nice to dry the clothes off."

"You're welcome. I really like washing clothes."

This scene is from the movie The Secret World of Arrietty , which tells the daily life and interactions of small people and is really heartwarming and tearjerking.

Assume that Arrietty is using poles instead of pulleys to hang the clothes, which can be modeled as the picture below:

In the picture, a light and unstretchable rope is fixed at point $a,b$ of the fixed poles $M$ and $N$ . The hook hanging the clothes and the rope are both smooth .

If Arrietty wants to move the clothes to the left, she can move the right end of the rope from $b$ to $b'$ . After the system is balanced again, how will the tension of the rope change?

The tension will increase. The tension will decrease. The tension won't change.

4 solutions

Jonathan Dinkelbach
Aug 23, 2020

The force of the clothes (gravity) is compensated by two forces from the hook towards a and from the hook towards b (resp. later b’). These two forces in the direction of the rope induce the tension.

Now we know that the system is in balance, which means the two forced to the right and to the left are equally strong and therefore the angles of the rope with a horizontal line are equal as well (the sum of the two forces is perpendicular to the horizontal line).

This holds for any position of b’ as well. Now the rope has a fixed length (not stretchable), and together with the angle condition this means that the new rope position (from hook to b’) is parallel to the original. So the angles stay constant and the tension does not change.

didn't understand

Neeraja Raj - 9 months, 3 weeks ago

the tension depends on the angle. and the angle stays the same when the system is in balance.

num IC - 9 months, 2 weeks ago

You're right! It was my belief, at first, that the angles would decrease, but that is not the case.

Luis Viñé - 9 months, 2 weeks ago

Does the tension towards point a and point b(or b') necessarily have to be equal to each other? Their horizontal components need to cancel each other out, but their vertical components don't have to be related to each other, right? The sum of the vertical components just need to cancel out the weight of the cloth in order for the system to be in balance, so I don't see how the angles necessarily need to be equal to each other.

준희 이 - 9 months, 1 week ago

Good point!

Julie K - 7 months, 2 weeks ago

Joseph Traverso
Nov 21, 2020

It’s still has the same load, so the tension must not change after balancing

Ravand H.I.M
Aug 23, 2020

The question says after being balanced, so that means that it went back to the original that had no tension to begin with. It's basically like displacements, where if you go around in a circle- start and finish at the same point- your displacement is gonna be 0m. Using this logic with tension we can understand that even after adding tons of forces to the rope but at the end remove it all, it will be like nothing ever happened.

A balanced system implies the net force is null, but here tension is only part of it.

alazrabed . - 9 months, 3 weeks ago

Cas L
Dec 26, 2020

I just thought that, “the tension cannot increase or decrease because the poles are not changing their distances. They’re stationary.” Then it is not possible for the rope’s tension to change and we are not adding or removing anything from the rope for the tension to change.

but the distance between the 2 poles has increased, the angle of slop have diminished making the angle closer to 90 degrees thus adding tension to the line

Alex Sittig - 4 months, 3 weeks ago

The Secret World of Arrietty

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