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A mass is suspended at the bottom of two springs in series having stiffness 10 N/mm and 5 N/mm. The equivalent spring stiffness of the two springs is nearly
- a)0.3 N/mm
- b)3.3 N/mm
- c)5 N/mm
- d)15 N/mm
Correct answer is option 'D'. Can you explain this answer?
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A mass is suspended at the bottom of two springs in series having stif...
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A mass is suspended at the bottom of two springs in series having stif...
Analysis:
When two springs are connected in series, the equivalent spring stiffness can be calculated by adding the reciprocals of the individual spring stiffnesses.
Solution:
Given:
Stiffness of the first spring, k1 = 10 N/mm
Stiffness of the second spring, k2 = 5 N/mm
The equivalent spring stiffness, keq can be calculated as follows:
1/keq = 1/k1 + 1/k2
Substituting the given values:
1/keq = 1/10 + 1/5
Simplifying the equation:
1/keq = (1+2)/10
1/keq = 3/10
Taking the reciprocal of both sides:
keq = 10/3 N/mm
Converting the units to N/m:
keq = (10/3) * (1000/1) N/m
keq = 10000/3 N/m
keq ≈ 3333.33 N/m (rounded to one decimal place)
Answer:
The equivalent spring stiffness of the two springs in series is approximately 3333.33 N/m, which is closest to option D.
When two springs are connected in series, the equivalent spring stiffness can be calculated by adding the reciprocals of the individual spring stiffnesses.
Solution:
Given:
Stiffness of the first spring, k1 = 10 N/mm
Stiffness of the second spring, k2 = 5 N/mm
The equivalent spring stiffness, keq can be calculated as follows:
1/keq = 1/k1 + 1/k2
Substituting the given values:
1/keq = 1/10 + 1/5
Simplifying the equation:
1/keq = (1+2)/10
1/keq = 3/10
Taking the reciprocal of both sides:
keq = 10/3 N/mm
Converting the units to N/m:
keq = (10/3) * (1000/1) N/m
keq = 10000/3 N/m
keq ≈ 3333.33 N/m (rounded to one decimal place)
Answer:
The equivalent spring stiffness of the two springs in series is approximately 3333.33 N/m, which is closest to option D.
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A mass is suspended at the bottom of two springs in series having stiffness 10 N/mm and 5 N/mm. The equivalent spring stiffness of the two springs is nearlya)0.3 N/mmb)3.3 N/mmc)5 N/mmd)15 N/mmCorrect answer is option 'D'. Can you explain this answer?
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