if a string of stiffness k is cut into two parts A and B of length lalb=23,then the stiffness of spring A is given by
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A spring is cut into two parts of length La and Lb
Also given that La : Lb = 2 : 3
If the length of spring is L , then La = 2L/5
And length of B , Lb = 3L/5
We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .
e.g., K α 1/L
If intial spring constant is k then,
kL = KaLa = KbLb
Then, Ka = k/(2/5) = 5k/2
And Kb = k/(3l/5) = 5k/3
Hence, stiffness of A is given by 5k/2
Also given that La : Lb = 2 : 3
If the length of spring is L , then La = 2L/5
And length of B , Lb = 3L/5
We know, for spring force , spring constant or stiffness of spring is inversely proportional to length of spring .
e.g., K α 1/L
If intial spring constant is k then,
kL = KaLa = KbLb
Then, Ka = k/(2/5) = 5k/2
And Kb = k/(3l/5) = 5k/3
Hence, stiffness of A is given by 5k/2
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