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Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms?
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Spring 40 mm long stretched by the application of force if 10 Newton f...
To calculate the work done in stretching a spring, we use Hooke's Law, which states that the force required to stretch or compress a spring is proportional to the distance it is stretched or compressed. The mathematical expression for Hooke's Law is:
Work Done in Stretching the Spring
The formula for work done (W) in stretching a spring is given by:
\[ W = \frac{1}{2} k x^2 \]
Where:
- \( W \) = work done
- \( k \) = spring constant (N/m)
- \( x \) = stretch distance (m)
Finding the Spring Constant (k)
Given that a force of 10 Newtons is required to stretch the spring by 1 mm (0.001 m):
- From Hooke's Law: \( F = kx \)
- Substituting the values: \( 10 = k \times 0.001 \)
- Therefore, \( k = \frac{10}{0.001} = 10000 \, \text{N/m} \)
Calculate Work Done for 40 mm Stretch
Now, to find the work done when the spring is stretched through 40 mm (0.04 m):
- Substitute \( k \) and \( x \) into the work formula:
\[ W = \frac{1}{2} \times 10000 \times (0.04)^2 \]
- Calculating the work:
\[ W = \frac{1}{2} \times 10000 \times 0.0016 \]
\[ W = 8 \, \text{Joules} \]
Conclusion
Thus, the work done in stretching the spring through 40 mm is **8 Joules**. This calculation illustrates the linear relationship between the force applied and the distance stretched, confirming the principles of elasticity in springs.
Work Done in Stretching the Spring
The formula for work done (W) in stretching a spring is given by:
\[ W = \frac{1}{2} k x^2 \]
Where:
- \( W \) = work done
- \( k \) = spring constant (N/m)
- \( x \) = stretch distance (m)
Finding the Spring Constant (k)
Given that a force of 10 Newtons is required to stretch the spring by 1 mm (0.001 m):
- From Hooke's Law: \( F = kx \)
- Substituting the values: \( 10 = k \times 0.001 \)
- Therefore, \( k = \frac{10}{0.001} = 10000 \, \text{N/m} \)
Calculate Work Done for 40 mm Stretch
Now, to find the work done when the spring is stretched through 40 mm (0.04 m):
- Substitute \( k \) and \( x \) into the work formula:
\[ W = \frac{1}{2} \times 10000 \times (0.04)^2 \]
- Calculating the work:
\[ W = \frac{1}{2} \times 10000 \times 0.0016 \]
\[ W = 8 \, \text{Joules} \]
Conclusion
Thus, the work done in stretching the spring through 40 mm is **8 Joules**. This calculation illustrates the linear relationship between the force applied and the distance stretched, confirming the principles of elasticity in springs.
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Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms?
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Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms?.
Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spring 40 mm long stretched by the application of force if 10 Newton force required to stretch the spring through one mm then work then is stretching the spring through 40mms?.
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