# The Wicked King and the Beautiful Princess - Tension

• Talha Temuri
In summary, the conversation discusses a story of a wicked king who locks up his beautiful daughter in a tall tower, and her lover, a brave prince, who attempts to rescue her. The prince constructs a pulley system using a bucket and rope to reach the top of the tower, but is unable to let go of the rope to embrace the princess without falling. He then discovers a metal hook on the tower wall and ties the rope to it, causing the supporting beam to break and the prince to fall. The question is raised about how the king knew the prince would fall, and references to a similar problem discussed by Gauss and his teacher are mentioned. The solution involves calculating the tension in the rope and the force on the beam using an At
Talha Temuri
I have no idea where to begin. Any help would be appreciated.

Once upon a time there was a terribly wicked King who had a daughter who was very beautiful. The daughter was in love with a handsome prince, and before long the prince and the princess had become inseparable. The King, however, was wicked and did not believe in happiness and so he had his daughter locked up in a prison at the top of a tall tower.

The prince learned of this and was determined to rescue the one he loved, so he started out for the tower where the unhappy princess sat imprisoned. When he arrived at the base of the tower the prince looked up and noticed that there was a wooden beam protruding from the top of the structure. He immediately contrived a method to use this, to reach his princess. He attached a sturdy bucket, he found nearby, to one end of a very long rope and to the other end he tied a stone. Then with a mighty heave he threw the stone across the top of the beam so that the rope was looped across the top of the beam. The prince had thus constructed a simple pulley. He then stepped into the bucket and proceeded to hoist himself up. (See the well-drawn diagram)

In due time the prince reached the top and was rewarded with a long embrace by the King's daughter. The prince, however, could not return the embrace, nor could he begin his work to release the princess, since letting go of the rope would cause the bucket to fall. So he began searching for a way to fix the rope to the tower wall. Luck seemed to be smiling on the young man because close by, he discovered a metal hook embedded in the stonewall. The prince tugged on the hook with one hand (the other hand holding the rope tightly), and finding it secure, he proceeded to tie the rope to the hook. But the instant he did that, the supporting beam broke and the bucket, together with the poor prince, came crashing to the ground. The King, who was very wicked, also happened to know his physics very well (no connection between the two), and had originally designed the beam to support the weight of the prince and the weight of the bucket, but no more How did the King know the prince would fall? Show using diagram and equations.

Can you give a reference to where you got this problem from?

Also, you need to use the homework template--you need to give the equations that you think might apply and show your own attempt at a solution. Just saying "I have no idea where to begin" is not enough.

Talha Temuri said:
I have no idea where to begin.
Yet forum rules require you to show some attempt.
Start with two diagrams, one showing the prince, bucket, rope and beam before he tied the rope to the hook, the other after he has tied it and let go the rope.
In each, show the forces on the rope, on the prince+bucket, and on the beam.
Post your diagrams, and any equations you can develop.

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I agree that the template should be followed, but I am not sure equations are needed. The king had
Talha Temuri said:
... originally designed the beam to support the weight of the prince and the weight of the bucket, but no more.
Just look at the picture. There is more than just the prince and the bucket producing tension in the rope.

It seems to me that I read that Gauss had an argument with his teacher about a similar problem.
"if a person sitting on a bench with a rope attached to the bench and passing over a pulley tried
to raise himself by pulling on the other end of the rope, what force would be required?"
Apparently, he went home and tested this out in a barn.
The teacher's answer was W and Gauss' answer was W/2.

Raising generally implies acceleration unless done at constant speed. I would rephrase the question to ask "If a person raised himself above the bench at some fixed height, with what force does he need to pull on the rope to stay at that height? Then Gauss's answer would be correct.

Even if the force required is somewhat greater than W/2 and the force on the pulley (beam) is somewhat greater
than W, what is the force on the pulley (beam) when the rope is attached to the hook and the prince let's go of the rope?

J Hann said:
Even if the force required is somewhat greater than W/2 and the force on the pulley (beam) is somewhat greater
than W, what is the force on the pulley (beam) when the rope is attached to the hook and the prince let's go of the rope?
You have two ropes each puling down with tension T on the beam. As long as the rope is under tension, the force on the beam is 2T. This can be idealized as an Atwood's machine situation with a well known answer for the tension T. On one side you have W1 = Wprince + Wbucket and on the other side you have W2 = Wstone.

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@kuruman, @J Hann , I'm not sure what you are debating in this thread but you are in danger of laying out the solution for the OP (who has not resurfaced since post #1), or of obscuring it with irrelevancies.

The acceleration can be made effectively irrelevant by making it arbitrarily small.

The Gauss anecdote concerns the tension in the rope rather than the force on the beam. It might be helpful, or it might be confusing. We should wait and see where the OP is stuck.

As I read the question, the stone was only used to get the rope over the beam and now lies harmlessly on the ground.

haruspex said:
As I read the question, the stone was only used to get the rope over the beam and now lies harmlessly on the ground.

That would make sense with the description in words, but it is not consistent with the picture given in the OP, which shows the stone hanging in the air as the prince pulls himself up. Which might just mean the picture and the words are inconsistent and whoever put the problem together didn't notice. Since we still don't know where this comes from, we don't know how reliable the source is.

haruspex said:
We should wait and see where the OP is stuck.

To make that easier, I have partially locked down the thread awaiting a further post from the OP.

PeterDonis said:
That would make sense with the description in words, but it is not consistent with the picture given in the OP,
You are right, the illustration violates this statement:
Talha Temuri said:
weight of the prince and the weight of the bucket, but no more

## 1. What is the main conflict in "The Wicked King and the Beautiful Princess - Tension"?

The main conflict in "The Wicked King and the Beautiful Princess - Tension" is between the titular characters, the wicked king and the beautiful princess. The king desires power and control, while the princess yearns for freedom and equality. This creates tension between them and drives the plot forward.

## 2. How does the tension between the wicked king and the beautiful princess impact the story?

The tension between the wicked king and the beautiful princess drives the story forward and creates a sense of urgency and conflict. It also highlights the power dynamics and societal issues present in the kingdom, as well as the personal struggles and desires of the characters.

## 3. Is there a resolution to the tension between the wicked king and the beautiful princess?

Without giving away spoilers, it can be said that the tension between the wicked king and the beautiful princess is resolved in some way by the end of the story. However, the exact nature of this resolution and whether it is a happy or tragic one is up to interpretation.

## 4. What themes are explored in "The Wicked King and the Beautiful Princess - Tension"?

Some of the themes explored in "The Wicked King and the Beautiful Princess - Tension" include power and control, societal expectations and norms, love and sacrifice, and the consequences of actions and decisions.

## 5. How does the tension in this story relate to real-world issues and conflicts?

The tension between the wicked king and the beautiful princess can be seen as a reflection of real-world power struggles and societal issues. It can also serve as a commentary on the consequences of greed, oppression, and inequality. The story's resolution can offer insights and lessons on how to address and overcome these issues in our own lives and society.

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