SUSPENSION BRIDGE PROBLEM

-
Question of the suspension bridge

 The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Think of the problem as a real problem that you have to calculate the length of the wire. It is a very interesting problem that helps one to understand where mathematics is used in real life situation.




  • It would be easy to visualize the problem if we have a diagram. So, let us draw a diagram.


SUSPENSION BRIDGE PROBLEM

  • Now let us plot a coordinate graph for this diagram









If we now solve using the coordinates of the parabola would get the answer. 

 Let us take the point ( 50, 24 ) and solving we get 

Again using the point ( 18, y ) and solving we get 

This is the length between the point ( 18, y ) and the x-axis.
Therefore we have to add the length of the wire below the axis to this length so that we could calculate the length of the whole wire. 

Hence, the length of the wire is 3.11 + 6 = 9.11 m ( approximate ).

Comments

Post a Comment

Popular posts from this blog

DOT PUZZLE ( CONNECT ALL THE DOTS WITHOUT LIFTING THE PEN AND WITH ONLY FOUR STRAIGHT LINES WITHOUT ANY OVERLAP )

-
Image
Here we would solve a dot puzzle Consider the figure below Connect all the dots without lifting the pen with only 4 straight lines and the lines do not overlap. Here are some examples already done for you but not been solved because some dots left to be crossed. You could see that some dots have been left to be crossed by the line. So do you think you could solve it. Let us try one more time. Now, what do you see, the puzzle has been solved with the required conditions. Find out some more solutions to this question.
Read more

EULER TRAIL PUZZLE

-
Image
What is an Euler trail ? An Euler trail ( Euler path ) is a trail in a finite graph which visits every edge exactly once. An Euler trail is a walk on the edges of a graph which uses each edge exactly once. Euler trail is also called an Euler chain , Euler walk , Euler path . Here is the puzzle as you could see in the picture. Your job is to cross each line exactly once without lifting your pen.  In the following figure consider every marked line as a single line and each must be crossed once without lifting you pen. Here are some examples already done, but in each case, one line is left ( marked red ) to be crossed . See the figures. Have you got the solution ? well, this is impossible to do however hard you try.  Explanation Consider the figure below and find the numbers of line reaching the centre of each box. In the figure you could see that there are three centre points with odd number of lines
Read more