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A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :
- a)k/4
- b)k/2
- c)2k
- d)4k
Correct answer is option 'A'. Can you explain this answer?
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A helical spring has N turns of coil of diameter D, and a second sprin...
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A helical spring has N turns of coil of diameter D, and a second sprin...
Introduction:
In this question, we are given two helical springs made of the same wire diameter and material. The first spring has N turns of coil with diameter D, while the second spring has N/2 turns of coil with diameter 2D. We need to determine the stiffness of the second spring in terms of the stiffness of the first spring.
Understanding Stiffness:
The stiffness of a spring is a measure of its ability to resist deformation when subjected to an external force. It is defined as the ratio of the force applied to the displacement produced.
Analysis:
To determine the stiffness of the second spring, we need to compare it with the first spring. Let's consider the first spring and analyze its stiffness.
Stiffness of the First Spring:
The stiffness of a helical spring is given by the formula:
k = (Gd^4)/(8D^3n),
where k is the stiffness, G is the modulus of rigidity of the material, d is the wire diameter, D is the coil diameter, and n is the number of turns.
Stiffness of the Second Spring:
Now, let's analyze the stiffness of the second spring. It has N/2 turns of coil with diameter 2D and the same wire diameter as the first spring.
Comparing the Springs:
To compare the stiffness of the two springs, we need to compare the terms in the formula for stiffness.
Comparing the Number of Turns:
The first spring has N turns, while the second spring has N/2 turns. Comparing these terms, we can see that the second spring has half the number of turns as the first spring.
Comparing the Coil Diameter:
The first spring has a coil diameter of D, while the second spring has a coil diameter of 2D. Comparing these terms, we can see that the second spring has twice the coil diameter as the first spring.
Calculating the Stiffness:
Now, let's calculate the stiffness of the second spring using the formula mentioned earlier.
For the second spring:
k' = (Gd^4)/(8(2D)^3(N/2))
= (Gd^4)/(8D^3N/8)
= (Gd^4)/(D^3N)
= (1/8)(Gd^4)/(D^3N)
= (1/8)k
Hence, the stiffness of the second spring is k/8, which is equivalent to k/4.
Answer:
Therefore, the correct answer is option 'A' - k/4.
In this question, we are given two helical springs made of the same wire diameter and material. The first spring has N turns of coil with diameter D, while the second spring has N/2 turns of coil with diameter 2D. We need to determine the stiffness of the second spring in terms of the stiffness of the first spring.
Understanding Stiffness:
The stiffness of a spring is a measure of its ability to resist deformation when subjected to an external force. It is defined as the ratio of the force applied to the displacement produced.
Analysis:
To determine the stiffness of the second spring, we need to compare it with the first spring. Let's consider the first spring and analyze its stiffness.
Stiffness of the First Spring:
The stiffness of a helical spring is given by the formula:
k = (Gd^4)/(8D^3n),
where k is the stiffness, G is the modulus of rigidity of the material, d is the wire diameter, D is the coil diameter, and n is the number of turns.
Stiffness of the Second Spring:
Now, let's analyze the stiffness of the second spring. It has N/2 turns of coil with diameter 2D and the same wire diameter as the first spring.
Comparing the Springs:
To compare the stiffness of the two springs, we need to compare the terms in the formula for stiffness.
Comparing the Number of Turns:
The first spring has N turns, while the second spring has N/2 turns. Comparing these terms, we can see that the second spring has half the number of turns as the first spring.
Comparing the Coil Diameter:
The first spring has a coil diameter of D, while the second spring has a coil diameter of 2D. Comparing these terms, we can see that the second spring has twice the coil diameter as the first spring.
Calculating the Stiffness:
Now, let's calculate the stiffness of the second spring using the formula mentioned earlier.
For the second spring:
k' = (Gd^4)/(8(2D)^3(N/2))
= (Gd^4)/(8D^3N/8)
= (Gd^4)/(D^3N)
= (1/8)(Gd^4)/(D^3N)
= (1/8)k
Hence, the stiffness of the second spring is k/8, which is equivalent to k/4.
Answer:
Therefore, the correct answer is option 'A' - k/4.
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A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer?
Question Description
A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. 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 A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. 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 A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer?.
A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. 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 A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. 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 A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer?.
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A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A helical spring has N turns of coil of diameter D, and a second spring, made of same wire diameter and of same material, has N/2 turns of coil of diameter 2D. If the stiffness of the first spring is k, then the stiffness of the second spring will be :a)k/4b)k/2c)2kd)4kCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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