Question
It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 6 m . Find the force constant of the spring.
The spring’s force constant is
.
(Type an integer or a simplified fraction.)
The spring’s force constant is
(Type an integer or a simplified fraction.)
Ask by Montgomery Estrada. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The spring’s force constant is
.
Solution
The work done in stretching a spring by a displacement
from its natural length is given by
- The spring is stretched from 1 m to 6 m, so the displacement is
- Substitute the given work
J and m into the work formula:
- Simplify the equation:
- Solve for
by multiplying both sides by :
- Simplify the fraction:
Thus, the spring’s force constant is
.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Mind Expander
To find the force constant
of the spring, we can use the formula for the work done on a spring, which is given by:
Here,
is the work done (1900 J),
is the force constant, and
is the extension of the spring from its natural length. In this case, the natural length is 1 m, and the stretched length is 6 m, so:
Now substituting the values into the formula:
This simplifies to:
Solving for
:
So, the spring’s force constant is
.