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

[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 Alot!

 

[Chi Meson]

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 Alot!

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."

 

[Fuego]

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.

 

[daodude1987]

Thanks a bunch! Everything is much clearer now!