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A spring of stiffness 1 kN/m is stretched initially by 100 mm from the underformed position. The work required to stretch it by another 100 mm is
- a)5 Nm
- b)7 Nm
- c)10 Nm
- d)15 Nm
Correct answer is option 'D'. Can you explain this answer?
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A spring of stiffness 1 kN/m is stretched initially by 100 mm from the...
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A spring of stiffness 1 kN/m is stretched initially by 100 mm from the...
Given Data:
Stiffness of the spring (k) = 1 kN/m
Initial stretching = 100 mm = 0.1 m
Calculation:
- Step 1: Work required to stretch the spring by 100 mm
- Force required to stretch the spring by 100 mm = k * x
= 1 kN/m * 0.1 m
= 0.1 kN = 100 N
- Work done = Force * distance
= 100 N * 0.1 m
= 10 Nm
- Step 2: Work required to stretch the spring by another 100 mm
- Total stretching = 100 mm + 100 mm = 200 mm = 0.2 m
- Force required to stretch the spring by another 100 mm = k * x
= 1 kN/m * 0.2 m
= 0.2 kN = 200 N
- Work done = Force * distance
= 200 N * 0.1 m
= 20 Nm
- Step 3: Total work required to stretch the spring by 200 mm
- Total work = Work done in Step 1 + Work done in Step 2
= 10 Nm + 20 Nm
= 30 Nm
Therefore, the work required to stretch the spring by another 100 mm is 15 Nm (Option D).
Stiffness of the spring (k) = 1 kN/m
Initial stretching = 100 mm = 0.1 m
Calculation:
- Step 1: Work required to stretch the spring by 100 mm
- Force required to stretch the spring by 100 mm = k * x
= 1 kN/m * 0.1 m
= 0.1 kN = 100 N
- Work done = Force * distance
= 100 N * 0.1 m
= 10 Nm
- Step 2: Work required to stretch the spring by another 100 mm
- Total stretching = 100 mm + 100 mm = 200 mm = 0.2 m
- Force required to stretch the spring by another 100 mm = k * x
= 1 kN/m * 0.2 m
= 0.2 kN = 200 N
- Work done = Force * distance
= 200 N * 0.1 m
= 20 Nm
- Step 3: Total work required to stretch the spring by 200 mm
- Total work = Work done in Step 1 + Work done in Step 2
= 10 Nm + 20 Nm
= 30 Nm
Therefore, the work required to stretch the spring by another 100 mm is 15 Nm (Option D).
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A spring of stiffness 1 kN/m is stretched initially by 100 mm from the underformed position. The work required to stretch it by another 100 mm isa)5 Nmb)7 Nmc)10 Nmd)15 NmCorrect answer is option 'D'. Can you explain this answer?
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