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If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).
Correct answer is '8.00 to 8.50'. Can you explain this answer?
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If the wire diameter of a compressive helical spring is increased by 2...
Understanding Spring Stiffness
The stiffness of a helical spring is influenced by various factors, including the wire diameter. The formula for spring stiffness (k) is given by:
k = (G * d^4) / (8 * D^3 * n)
Where:
- G = Modulus of rigidity
- d = Wire diameter
- D = Mean coil diameter
- n = Number of active coils
Impact of Wire Diameter Increase
When the wire diameter (d) is increased by 2%, the new wire diameter becomes:
New d = d * (1 + 0.02) = 1.02d
To find the change in spring stiffness:
1. **Calculate the new stiffness (k')**:
k' = (G * (1.02d)^4) / (8 * D^3 * n)
2. **Express stiffness in terms of old stiffness (k)**:
k' = (G * d^4 * (1.02^4)) / (8 * D^3 * n)
k' = k * (1.02^4)
3. **Calculate the percentage increase in stiffness**:
- First, compute 1.02^4:
- 1.02^4 ≈ 1.08243216 (approximately 8.24%)
- Therefore, the change in spring stiffness is:
Percentage change = (k' - k) / k * 100
- This gives approximately 8.24%.
Conclusion
Thus, increasing the wire diameter by 2% results in a spring stiffness change of about 8.00 to 8.50%, confirming the correct answer range.
The stiffness of a helical spring is influenced by various factors, including the wire diameter. The formula for spring stiffness (k) is given by:
k = (G * d^4) / (8 * D^3 * n)
Where:
- G = Modulus of rigidity
- d = Wire diameter
- D = Mean coil diameter
- n = Number of active coils
Impact of Wire Diameter Increase
When the wire diameter (d) is increased by 2%, the new wire diameter becomes:
New d = d * (1 + 0.02) = 1.02d
To find the change in spring stiffness:
1. **Calculate the new stiffness (k')**:
k' = (G * (1.02d)^4) / (8 * D^3 * n)
2. **Express stiffness in terms of old stiffness (k)**:
k' = (G * d^4 * (1.02^4)) / (8 * D^3 * n)
k' = k * (1.02^4)
3. **Calculate the percentage increase in stiffness**:
- First, compute 1.02^4:
- 1.02^4 ≈ 1.08243216 (approximately 8.24%)
- Therefore, the change in spring stiffness is:
Percentage change = (k' - k) / k * 100
- This gives approximately 8.24%.
Conclusion
Thus, increasing the wire diameter by 2% results in a spring stiffness change of about 8.00 to 8.50%, confirming the correct answer range.
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If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer?
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If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer?.
If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).Correct answer is '8.00 to 8.50'. Can you explain this answer?.
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