Skip to main content
Sister Publication Links
  • Rubber & Plastics News
Subscribe
  • My Account
  • LogIn
  • News
  • Technology Focus
    • Features
    • Technical Papers
    • Analysis: Rubber mixing plants of the future
      Analysis: US probes dumping by ESBR suppliers
      Opinion: Tire labels stuck in a rut
      Analysis: NR pricing takes one step forward, two steps back
    • Technical paper: Varying Si-substituents for rubber silanes
      White paper: Role of tire innerliners in improving 'in-use rolling resistance'
      White paper: Why tire air retention matters now more than ever
      Nippon Soda: Use of 1,2-polybutadiene in CSM rubber applications
  • Events
    • ERJ Events
    • ERJ Livestreams & Webinars
    • Industry Events
    • Journey to Automation Awards 2020
      Sustainability: Top 10 E4S projects table
  • Maps & Reports
  • People
  • Directory
  • Digital Edition
  • Brainiac
MENU
Breadcrumb
  1. Home
  2. Brainiac
November 30, 2020 08:07 AM

ERJ Brainteaser: December

ERJ
  • Tweet
  • Share
  • Share
  • Email
  • More
    Print
    Question 4: Connected cities 

     

    Find the connection between these cities (ordered alphabetically) and fill in the missing two.

    Antwerp, ___, Barcelona, ___, Melbourne, Montreal, Munich, St. Louis, Sydney. 

    Answer: After the year we’ve all had, it is not surprising that many readers have turned their minds to more solid (and, perhaps. liquid) matters. So it is extra well done to last-Brainiacs-standing Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; and John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK. They identified that these, along with Atlanta and Los Angeles, are non-capital cities to have hosted the summer Olympics.

    Wishing all our readers - Brainics and non-Brainiacs alike - a very Happy Christmas and a great New Year!

    Next teaser in early January, when we will also announce the winners in the prestigious Brainiac of the Year Awards.
     

     

     

     

    Question 3: Tennis ball tests

     

    At a tennis ball manufacturing company, materials scientists are testing their latest product range for bounce.
    In one experiment, a ball is thrown vertically upwards with a speed of 16 m s−1 from a point 80 metres above the ground.
    The test guys have to work out the speed with which the ball strikes the ground as well as the total time the ball is more than 85 metres above the ground.
    When it lands, the ball rebounds with 20% of the speed with which it strikes the ground. The team then try to work out the greatest height reached by the ball when it rebounds.

    What should be the results of the three tests?l

    Answer: This really was one of our tougher teasers, so hats off to everyone who had ago. And, extremely well done to the following ace readers, who skilfully worked out the answers at: around 43m s−1, 2.6s, and 3.7m (solutions below): Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria;  John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; and Michele Girardi, Scame  Mastaf Spa, Suisio, Italy.

    Solutions

    John Bowen
    Mr Newton comes in handy here, as we need to use the equations of motion where acceleration due to gravity is taken as 9.81ms-2
    To calculate the speed the ball hits the ground, we need to calculate the initial height above the 80m start:
    v.sqd-u.sqd =2fs: at the top velocity = 0, so 16 sqd = 2fs; 256 = 2*9.81*s = 13.05m.
    We use this equation again downwards to the ground to calculate velocity at impact: v. sqd = 2fs
    v.sqd = 2*9.81*93.05 [total fall is 80 + 13..05 above] = 1825.64
    v = 42.73ms-1 This is the velocity with which the ball hits the ground
    Use the same equation to calculate the rebound height: vsqd - usqd = 2fs; u = 8.55 [20% of impact speed], v = 0, f = -9.81
    73.1 = 2*9.81*s ; s = 3.73m
    To calculate the time above 85metres we use the Equation of motion s = ut + 1/2 f.tsqd and solve the resulting quadratic equation using the 80m starting point and height [s] of 5 m:
    5 = 16t - 1/2*9.81* tsqd
    Rearranging, 4.9*tsqd -16t + 5 = 0
    Applying the quadratic formula  [x = [-b+/-{sq rt [bsqd - 4ac]}/2a]
    t = 16 +/-SqRt[256-98]/9.8 = [16+/- 12.6]/9.8
    t = 0.35 [upwards] and 2.92 [downwards]
    So time above 85m high = 2.57 seconds

    Michele Girardi
    Y=Y0+V0*t-1/2.g.t^
    Y0=80
    g=10
     V0=16
    Y=80+16*t-5*t^2
    dY/dt = 16-10*t
    Using an excel file and the solver function to find Y equal to  85,85,0
    point         t       Y   dY/dt
    start       0,00   80,00   16,00
    cross 85    0,35   85,00   12,49
    max         1,60   92,80    0,00
    cross 85    2,85   85,00  -12,49
    ground      5,91    0,00  -43,08
    rebound V0' = 43.08*0,2 =   8,62
    after rebound
    V^2=V0'^2-2.g*Y
    V^2=8.62^2-20*Y
    Y  =(0-8.62^2)/(-20)
    max          Y=     3.72m
    Speed when the ball hits the ground : 43.1 m/s
    Time above 85 m  : 2.85-0,35 =    2.5s
    Heigth of rebound           3.72 m

     

    Bonus question

    What should the values of X be in the third row of this table?
     

    Table teaser

    The key to the equally tricky Bonus question was to identify that adding the numbers in the first two squares if each row (right to left) and then adding the digits to get the next number, ie in the third column. So, in the fourth row, 8+8=16, 1+6 =7 and 8+7=15, 1+5=6. Very well done here to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and Mehmet Koral, Erhardt-Leimer representative for Turkey, managing director, C&C Endüstriyel Danışmanlık, Eğitim ve Mümessillik Ltd, Göztepe, Istanbul, Turkey.

    New teaser on Monday
     

    Question 2: Can EU dig it? 

     

    Which country comes next in this series

    Belgium, Bulgaria, Cyprus, Denmark, Germany, _ , ….

    Answer: Only one correct reply to this week’s main teaser. So extra congratulations to Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria, who quickly worked out: “The answer is Hungary. (13th position in the alphabetical list of EU countries, applying prime numbers).”

     

     

    Question 1: Pentagon square


    From this diagram of a regular pentagon inside a square, can you work out the value of X?

    Pentagon

    Bonus question

    Which two numbers do not belong in this list of two-digit numbers?
    30, 31, 32, 33, 34, 36, 39, 40, 43, 44, 45, 46, 47, 48, 49…

    Answer: This one tripped up quite a few, with only a select set of readers correctly working out the answer at 54° (neat solutions below). Very well done to: Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Michele Girardi, Scame  Mastaf Spa, Suisio, Italy; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Francesco Parazzoli, R&D -  material development, new raw materials, Pirelli Tyre SpA, Milan, Italy;  Mehmet Koral, Erhardt-Leimer representative for Turkey, managing director, C&C Endüstriyel Danışmanlık, Eğitim ve Mümessillik Ltd, Göztepe, Istanbul, Turkey.

    There was only one correct reply to the Bonus question. First thing Monday, Stephan Paischer identified that 44 and 47 don’t belong, as they are phone prefixes on non-EU countries (UK and Norway). All the other are phone prefixes of EU countries.

    Solutions to main Pentagon question

    :1)    The base angle of a Pentagram is 108°.
    2)    The opposing angle is 72° (180-108).
    3)    The angles of the triangle on the down right side are 72+90+y=180°, y being therefore 18°.
    4)    The requested angle x is: 18+108+x=180°, x being therefore 54°.
    Stephan Paischer 

    Value of angle X = 54 deg [180 - 108 [internal angle of pentagon ]-18[remaining angle of triangle]
    John Bowen

    Let's call  O the center of the pentagon, A the top vertex and  B the origin of X
    - AOB =  360°/5 = 72°
    - OAB = OBA =  (180-72)/2 = 54°
    - X = OAB= 54°, since they are alternate interior angles Cheers
    Michele Girardi

    Exterior angle is 360/5 = 72 deg.
    Interior angle is 180-72 = 108 deg
    The angle opposite the exterior angle in the white triangle to the lower right in your diagram is 90 -72 = 18 deg
    Angle X therefore is 180 -18 -108 = 54 deg
    Andrew Knox

     

    New teaser on Monday
     

    RECOMMENDED FOR YOU
    ERJ Brainteaser: April
    ERJ Brainteaser: April
    ERJ Brainteaser: March
    ERJ Brainteaser: March
    ERJ Brainteaser: February
    ERJ Brainteaser: February
    Free Newsletters

    Breaking news and in-depth coverage of essential topics delivered straight to your inbox.

    Subscribe today

    Get the latest news impacting the European rubber industry, from breaking news to razor-sharp analysis, in print and online.

    Subscribe now
    Connect with Us
    • LinkedIn
    • Twitter
    • Youtube

    Logo
    Contact Us

    @ 2019 European Rubber Journal. 
    European Rubber Journal is published bi-monthly by NUERJ Ltd.

    Registered Office: Castle House, 89 High Street,
    Berkhamsted, Hertfordshire HP4 2DF, United Kingdom. 

    Tel. + 44 (0)203 196 0141 

    Registered No. 13104613 England

    Email: [email protected]

    Website www.european-rubber-journal.com

    Customer service 

    Tel. + 44 (0)203 196 0141 

     

    Resources
    • About us
    • Contact Us
    • Advertise with Us
    • Media Kit
    • Ad Choices Ad Choices
    • Sitemap
    Legal
    • Terms and Conditions
    • Privacy Policy
    • Privacy Request
    Copyright © 2021. NUERJ LTD. All Rights Reserved.
    • News
    • Technology Focus
      • Features
      • Technical Papers
    • Events
      • ERJ Events
      • ERJ Livestreams & Webinars
      • Industry Events
    • Maps & Reports
    • People
    • Directory
    • Digital Edition
    • Brainiac