Question
upstudy study bank question image url

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.)

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
  1. The spring is stretched from 1 m to 6 m, so the displacement is
  1. Substitute the given work J and m into the work formula:
  1. Simplify the equation:
  1. Solve for by multiplying both sides by :
  1. Simplify the fraction:
Thus, the spring’s force constant is .

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

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 .

Related Questions

Latest Physics Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy