Q.159. Length of a helix

Question 159.
What is the length of the wire needed to make a spring of length L, diameter D and  number of turns, N.

Answer 159.
Let
L = length of the spring

D = diameter of the spring and
N = number of turns of the spring.

Now, the distance between successive turns = L/N
If the cylindrical surface of the spring is cut open along the length, it will be a rectangle with one end of the spring at one corner and the other end of one turn at the diagonally opposite corner of the rectangle of length = πD and width = L/N
=> length of one turn of the helix = √[(πD)^2 + (L/N)^2]
=> Total length of the wire needed to make the spring
= N * √[(πD)^2 + (L/N)^2]
= √[(πND)^2 + L^2].

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