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If both the mean coil diameter and wire diameter of a helical compression or tension spring be doubled, then the deflection of the spring close coiled under same applied load will
- a)be doubled
- b)be halved
- c)increase four times
- d)get reduced to one-fourth
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
When both the mean coil diameter and wire diameter of a helical compression or tension spring are doubled, the following changes occur:
- The mean coil diameter (mean diameter of the spring) is doubled, which means the length of the spring is increased.
- The wire diameter (diameter of the wire used to make the spring) is doubled, which means the cross-sectional area of the wire is increased.
As a result of these changes, the following effects are observed on the spring:
- The spring rate (load per unit deflection) is reduced by a factor of 4, since the cross-sectional area of the wire is increased by a factor of 4 (doubling the diameter results in a 4-fold increase in the cross-sectional area).
- The solid height (height of the spring when it is fully compressed without any gaps between the coils) is increased by a factor of 2, since the length of the spring is increased by a factor of 2 (doubling the mean diameter results in a 2-fold increase in the length of the spring).
- The free length (length of the spring when no load is applied) is also increased by a factor of 2, since the length of the spring is increased by a factor of 2.
Now, let's consider the deflection of the spring under the same applied load. Since the spring rate is reduced by a factor of 4, the deflection of the spring will be:
- Halved, since the load is the same and the spring rate is reduced by a factor of 4 (load = spring rate x deflection).
- Therefore, the correct answer is option B: the deflection of the spring will be halved.
When both the mean coil diameter and wire diameter of a helical compression or tension spring are doubled, the following changes occur:
- The mean coil diameter (mean diameter of the spring) is doubled, which means the length of the spring is increased.
- The wire diameter (diameter of the wire used to make the spring) is doubled, which means the cross-sectional area of the wire is increased.
As a result of these changes, the following effects are observed on the spring:
- The spring rate (load per unit deflection) is reduced by a factor of 4, since the cross-sectional area of the wire is increased by a factor of 4 (doubling the diameter results in a 4-fold increase in the cross-sectional area).
- The solid height (height of the spring when it is fully compressed without any gaps between the coils) is increased by a factor of 2, since the length of the spring is increased by a factor of 2 (doubling the mean diameter results in a 2-fold increase in the length of the spring).
- The free length (length of the spring when no load is applied) is also increased by a factor of 2, since the length of the spring is increased by a factor of 2.
Now, let's consider the deflection of the spring under the same applied load. Since the spring rate is reduced by a factor of 4, the deflection of the spring will be:
- Halved, since the load is the same and the spring rate is reduced by a factor of 4 (load = spring rate x deflection).
- Therefore, the correct answer is option B: the deflection of the spring will be halved.
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If both the mean coil diameter and wire diameter of a helical compression or tension spring be doubled, then the deflection of the spring close coiled under same applied load willa) be doubledb) be halvedc) increase four timesd) get reduced to one-fourthCorrect answer is option 'B'. Can you explain this answer?
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