This week's maths problem

Bewertung: 5 / 5

Details

Zugriffe: 25341

Problem of the week

exercice de maths de la semaine, math problem of the week, problema di matematica della settimana, सप्ताह के गणित समस्या, математическая задача недели, Ejercicio de matemáticas semanal, 今週の数学問題, בעיה מתמטית של השבוע, مشكلة الرياضيات الأسبوع, 这个周的数学问题, Haftanın matematik problemi, temporäre Problem vun der Woch, μαθηματικό πρόβλημα της εβδομάδας, math tatizo la wiki,

On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 12th. December 2024.

German version - Italian version - French version - Spanish version  Hungarian Version Russian version  --> 中文/Chinese <-- --> Ελληνικά   <-- Esperanto <-- --> Arabic <--

Series 68

problem 807

Based on an idea by Alexander Wolf, thank you.

Bernd attached two pulleys A and B to the ceiling of his room, 5 metres apart. He passed a 12 metre long nylon thread, which has a negligible dead weight, over these pulleys. With the help of Maria, Bernd attached 12 balls to the thread, each weighing 102 grams: 5 balls exactly in the centre of the thread at point C, 3 balls at the end of the thread below pulley A and 4 balls at the end of the thread below pulley B. Maria and Bernd carefully let go of the balls and watched as the thread with the balls moved for a while until they finally came to rest. Bernd exclaimed in amazement: ‘The shape that the thread has formed between the two pulleys reminds me a lot of Pythagoras’ triangle!’ Maria measured the side lengths of the triangle and was able to confirm Bernd's observation.
How long is the thread from pulley A to the three balls and how long from pulley B to the four balls? (2 blue dots)
Assume that the observation that the Pythagorean triangle has formed is correct. The three balls pull on pulley A with a force of 3 Newtons. How large is the proportion of this force that acts in the direction of pulley B? (4 blue points)
With what force does the deflection pulley A pull on the attachment in the ceiling? (+2 red points)

If we are not sure whether the triangle formed is actually the Pythagorean triangle, how can we calculate the force acting on the deflection pulley A in direction B without this assumption? (4 red points)

Deadline for solution is the 12th. December.

-> Enigma <--

https://www.schulmodell.eu/images/stories/mathe/horst/raetsel.php

Send your solutions to Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein!, if your answer contains attachments.

For text versions you can also use this form

--> here <--

Please give your full name so your points can be added to the score. If you would like to receive our weekly maths problem automatically you can

--> subscribe to our newsletter <-- .

Presently this newsletter is received by more than 2000 subscibers.

You can also send a paper copy of your solution as long as it is postmarked on or before the deadline.
adress:
Thomas Jahre
Paul-Jäkel-Straße 60
09113 Chemnitz
Germany

Links:

http://www.wurzel.org/

https://www.facebook.com/ArchimedesLab

http://people.missouristate.edu/lesreid/potw.html

post address: Thomas Jahre Chemnitzer Schulmodell Stollberger Straße 25 09119 Chemnitz Deutschland/Germany

QR-Code for this site