Solving for Unknown Mass Using Hooke's Law: Tips and Equations

  • Context: High School 
  • Thread starter Thread starter daodude1987
  • Start date Start date
  • Tags Tags
    Hooke's law Law
Click For Summary

Discussion Overview

The discussion revolves around using Hooke's Law to determine an unknown mass with a spring and known weights. Participants explore the methodology for measuring spring extension, calculating spring constant, and deriving mass from force measurements, focusing on practical application and graphical representation.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • A participant inquires about using a spring, ruler, and known masses to find an unknown mass, asking for equations and graphical methods.
  • Another participant explains Hooke's Law, stating that the restoring force is proportional to the extension of the spring and provides the formula F=-kx.
  • One participant suggests measuring the extension of the spring with known weights to establish a relationship between force and extension, emphasizing the importance of calculating the spring constant, k.
  • Another response details the process of plotting a graph of force against extension, noting that the graph should yield a straight line through the origin, indicating direct proportionality.
  • Participants discuss calculating the gradient of the graph to find k and using this value to determine the unknown mass based on its extension.

Areas of Agreement / Disagreement

Participants generally agree on the approach to use Hooke's Law and the method of graphing to find the unknown mass. However, there is no explicit consensus on the best way to present the equations or the graphical method, as the discussion includes various interpretations and suggestions.

Contextual Notes

Some assumptions about the accuracy of measurements and the linearity of the spring's response may not be explicitly stated. The discussion does not resolve potential variations in methodology or the precision of the derived equations.

Who May Find This Useful

This discussion may be useful for beginner physics students looking for practical applications of Hooke's Law and methods for determining mass using springs and known weights.

daodude1987
Hey guys, I'm a beginner physics student and I don't really know how to answer this question:

I have a spring, ruler,3 known masses, and 1 unknown mass.How would I find the unknown mass using these materials? Is it possible to solve using Hooke's Law? It would be very helpful if you guys can provide some equations or include any diagrams. Also how would I derive the needed equations from a graph? Thanks a lot!
 
Physics news on Phys.org
Originally posted by daodude1987
Hey guys, I'm a beginner physics student and I don't really know how to answer this question:

I have a spring, ruler,3 known masses, and 1 unknown mass.How would I find the unknown mass using these materials? Is it possible to solve using Hooke's Law? It would be very helpful if you guys can provide some equations or include any diagrams. Also how would I derive the needed equations from a graph? Thanks a lot!

Dude:

Hook's Law says "the restoring force of the spring is proportional to the extension or compression of the spring from its equilibrium." In formula form its F=-kx (the negative inticates that the force is in the opposite direction from the extension, x).

So, for every spring, there is a constant, k. Use your known masses and find how much of an "x" they will get on your sprin. Now you have three sets of F and x. How are they related? THrough "k".

Find k. Now you have k and you can measure the x of the unknown mass to get its weight (F).

Graphically: think "slope."
 
hang the 3 known masses one at a time on the end of the spring. for each mass, measure how much the spring extends.

convert the known masses into weight forces (multiply them by g (g = 9.8m/s/s).

now plot a graph of force against extension of the spring. you should have 3 points lying in a roughly straight line. draw the best fit line through those points; it should go through the origin.

because the graph is a straight line through the origin, extension and force applied are directly proportional. thus you can get an equation:

F = kx (this is hooke's law)

where F is the force applied, x is the extension and k is a constant of proportionality (the gradient of the graph).

calculate the gradient of the graph to find the value of k.

now put the unknown mass on the end of the spring and measure the extension. plug the extension into the above equation and you can work out the weight force applied by the mass. divide this by 9.8 to get the value of the mass.
 
Thanks a bunch! Everything is much clearer now!
 

Similar threads

Undergrad Is Hooke's law really not working, or is it me being dummy?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Understanding Newton's 2nd Law
  • · Replies 7 ·
Replies
7
Views
2K
High School Springboard physics questions for diving coach at YMCA
  • · Replies 12 ·
Replies
12
Views
3K
High School Why is there a negative in Hooke's Law (F = -kx)
  • · Replies 2 ·
Replies
2
Views
11K
High School Understanding Hooke's Law: Confusion with F=ks and F=-ks Explained
  • · Replies 4 ·
Replies
4
Views
2K
High School Inertial Mass vs Gravitational Mass
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Spring Constant in Hooke's Law
  • · Replies 3 ·
Replies
3
Views
2K
High School Why is Young's modulus constant below the limit of proportionality?
  • · Replies 23 ·
Replies
23
Views
5K
Graduate Can I determine mass & spring k from graph of wave, t, a, & vectors?
  • · Replies 1 ·
Replies
1
Views
2K
High School Newton’s second law as one complete law
  • · Replies 27 ·
Replies
27
Views
2K