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Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.
- a)7
- b)6
- c)5
- d)4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find total number coils in a spring having square and ground ends. Def...
Explanation: Deflection=8PDᵌN/Gd⁴ or N=4.4 or 5. Total coils=5+2(square grounded ends).
Most Upvoted Answer
Find total number coils in a spring having square and ground ends. Def...
To find the total number of coils in a spring, we need to use Hooke's law for a helical spring:
F = (G * d^4 * n) / (8 * D^3)
Where:
F = Load applied (1100N)
G = Modulus of rigidity (81370N/mm)
d = Diameter of the wire (unknown)
n = Total number of coils (unknown)
D = Mean diameter of the spring (unknown)
We also know that the deflection in the spring is 6mm, which can be related to the mean diameter using the formula:
6 = (64 * F * D^3) / (G * d^4)
Rearranging this equation to solve for D:
D^3 = (6 * G * d^4) / (64 * F)
Taking the cube root of both sides:
D = (6^(1/3) * d * (G / (64 * F)))^(1/3)
Now we can substitute this expression for D back into the original equation:
1100 = (G * d^4 * n) / (8 * ((6^(1/3) * d * (G / (64 * F)))^(1/3))^3)
Simplifying:
1100 = (G * d^4 * n) / (8 * ((6^(1/3) * d * (G / (64 * F)))^(3/3)))
1100 = (G * d^4 * n) / (8 * (6^(1/3) * d * (G / (64 * F)))^(1))
1100 = (G * d^4 * n) / (8 * 6^(1/3) * d * (G / (64 * F)))
Simplifying further:
1100 = (d^3 * n) / (48 * 6^(1/3))
Rearranging this equation to solve for n:
n = (1100 * 48 * 6^(1/3)) / d^3
Now we need to determine the value of d, which is the diameter of the wire. Unfortunately, this information is missing from the given data and cannot be calculated without further information.
F = (G * d^4 * n) / (8 * D^3)
Where:
F = Load applied (1100N)
G = Modulus of rigidity (81370N/mm)
d = Diameter of the wire (unknown)
n = Total number of coils (unknown)
D = Mean diameter of the spring (unknown)
We also know that the deflection in the spring is 6mm, which can be related to the mean diameter using the formula:
6 = (64 * F * D^3) / (G * d^4)
Rearranging this equation to solve for D:
D^3 = (6 * G * d^4) / (64 * F)
Taking the cube root of both sides:
D = (6^(1/3) * d * (G / (64 * F)))^(1/3)
Now we can substitute this expression for D back into the original equation:
1100 = (G * d^4 * n) / (8 * ((6^(1/3) * d * (G / (64 * F)))^(1/3))^3)
Simplifying:
1100 = (G * d^4 * n) / (8 * ((6^(1/3) * d * (G / (64 * F)))^(3/3)))
1100 = (G * d^4 * n) / (8 * (6^(1/3) * d * (G / (64 * F)))^(1))
1100 = (G * d^4 * n) / (8 * 6^(1/3) * d * (G / (64 * F)))
Simplifying further:
1100 = (d^3 * n) / (48 * 6^(1/3))
Rearranging this equation to solve for n:
n = (1100 * 48 * 6^(1/3)) / d^3
Now we need to determine the value of d, which is the diameter of the wire. Unfortunately, this information is missing from the given data and cannot be calculated without further information.
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Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct answer is option 'A'. Can you explain this answer?
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Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct 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 Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct 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 Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct answer is option 'A'. Can you explain this answer?.
Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct 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 Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct 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 Find total number coils in a spring having square and ground ends. Deflection in the spring is 6mm when load of 1100N is applied. Modulus of rigidity is 81370N/mm². Wire diameter and pitch circle diameter are 10mm and 50mm respectively.a)7b)6c)5d)4Correct answer is option 'A'. Can you explain this answer?.
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