a spring is stretched by 50mm by applying a force the work done by the spring is. if the force required for stretching 1 mm of the spring is 10N
Answers
Question:
A spring 50mm long spring is stretched by applying a force. If 10N force is required to stretch the spring through 1 mm, then work done in stretching the spring through 50mm is
Given:
Force (to stretch 1mm) = 10N
To Find:
Work done by stretching 50mm.
Solution:
Force constant,
∴ Work done by stretching the spring by 50mm is 12.5J.
Given:
Elongation
Force required for elongation
To find:
Work done by the spring to stretch the spring by .
Solution:
Step 1
We have been given that the force required by the spring to get elongated by a length of is
According to the Hooke's law, we have, the force required to elongate a spring by displacement is given by
Where, is the spring constant.
We have,
Hence, the spring constant of the spring is 10⁴ N/m.
Step 2
Now,
We know, the work done in stretching the spring is stored as the elastic potential energy in the spring.This value is given by
We have,
Hence, the work done by the spring will be
Final answer:
Hence, the work done by the spring in elongating the spring by 50 mm is 12.5 J.