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The inner spring of a compound helical spring is concentric with the outer one but is 8 mm shorter than that. The outer spring is of 30 mm mean diameter, has 12 coils with a wire diameter of 4 mm. If an axial load of 250 N compresses the outer spring by 20 mm, the stiffness of the inner spring is __________ N/mm.
(A) 8
(B) 8
    Correct answer is between ','. Can you explain this answer?
    Most Upvoted Answer
    The inner spring of a compound helical spring is concentric with the ...
    Given data:
    - Outer spring:
    - Mean diameter = 30 mm
    - Wire diameter = 4 mm
    - Number of coils = 12
    - Axial load = 250 N
    - Compression of outer spring = 20 mm

    Calculations:
    1. Calculate the mean diameter of the outer spring:
    Mean diameter = Outer diameter - Wire diameter
    Outer diameter = Mean diameter + Wire diameter
    Outer diameter = 30 mm + 4 mm = 34 mm

    2. Calculate the total number of turns in the outer spring:
    Total number of turns = Number of coils + 1
    Total number of turns = 12 + 1 = 13

    3. Calculate the length of the outer spring:
    Length of the outer spring = Total number of turns * Wire diameter
    Length of the outer spring = 13 * 4 mm = 52 mm

    4. Calculate the stiffness of the outer spring:
    Stiffness of the outer spring = Axial load / Compression
    Stiffness of the outer spring = 250 N / 20 mm = 12.5 N/mm

    5. Calculate the length of the inner spring:
    Length of the inner spring = Length of the outer spring - 8 mm
    Length of the inner spring = 52 mm - 8 mm = 44 mm

    6. Calculate the mean diameter of the inner spring:
    Mean diameter of the inner spring = Mean diameter of the outer spring - 2 * Wire diameter
    Mean diameter of the inner spring = 30 mm - 2 * 4 mm = 22 mm

    7. Calculate the total number of turns in the inner spring:
    Total number of turns in the inner spring = Length of the inner spring / Wire diameter
    Total number of turns in the inner spring = 44 mm / 4 mm = 11

    8. Calculate the stiffness of the inner spring:
    Stiffness of the inner spring = Stiffness of the outer spring * (Number of turns in the outer spring / Number of turns in the inner spring)
    Stiffness of the inner spring = 12.5 N/mm * (13 / 11) = 14.77 N/mm

    Therefore, the stiffness of the inner spring is approximately 14.77 N/mm.
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    The inner spring of a compound helical spring is concentric with the outer one but is 8 mm shorter than that. The outer spring is of 30 mm mean diameter, has 12 coils with a wire diameter of 4 mm. If an axial load of 250 N compresses the outer spring by 20 mm, the stiffness of the inner spring is __________ N/mm.(A) 8(B) 8Correct answer is between ','. Can you explain this answer?
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    The inner spring of a compound helical spring is concentric with the outer one but is 8 mm shorter than that. The outer spring is of 30 mm mean diameter, has 12 coils with a wire diameter of 4 mm. If an axial load of 250 N compresses the outer spring by 20 mm, the stiffness of the inner spring is __________ N/mm.(A) 8(B) 8Correct answer is between ','. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The inner spring of a compound helical spring is concentric with the outer one but is 8 mm shorter than that. The outer spring is of 30 mm mean diameter, has 12 coils with a wire diameter of 4 mm. If an axial load of 250 N compresses the outer spring by 20 mm, the stiffness of the inner spring is __________ N/mm.(A) 8(B) 8Correct answer is between ','. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The inner spring of a compound helical spring is concentric with the outer one but is 8 mm shorter than that. The outer spring is of 30 mm mean diameter, has 12 coils with a wire diameter of 4 mm. If an axial load of 250 N compresses the outer spring by 20 mm, the stiffness of the inner spring is __________ N/mm.(A) 8(B) 8Correct answer is between ','. Can you explain this answer?.
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