Module 3 Springs & Hooke's law Flashcards
What are tensile forces?
forces pulling, aka tension
What are compressing forces?
forces compressing an object
Define Hooke’s Law
The extension is directly proportional to the force exerted below the elastic limit
Formula for Hooke’s Law?
F=kx
F Force/N
k force or spring constant Nm^-1
x extension /m
What is the symbol for springs constant?
k
Another word for spring constant?
force constant
What is the shape of a force extension graph for a material that obeys Hooke’s law?
straight line through the origin
What does the gradient of a force extension graph equal?
the spring constant of the object k
What does the spring constant represent?
how easy or hard it is to deform an object (larger the constant the harder it is to deform)
Units for spring constant?
Nm^-1
What is extension?
Extended length - Original length
How is original length expressed?
L0 (measured with no mass)
Formula for extension? (the one using lengths)
x = L - L0
What is the elastic limit?
The maximum force a material can withstand without permanent deformation
What happens below the elastic limit if a spring is unloaded?
spring returns to original length
Describe how the shape of a force extension graph when a spring is loaded above its elastic limit?
graph becomes more flat and curved
What part of a force extension graph must be used to calculate the spring constant?
straight part/linear part
What happens when a weight is unloaded from a spring above the elastic limit?
permanent extension is observed in the spring
does not return to original length
Describe the setup/apparatus used to find the spring constant?
Clampstand with a clamp attached to the object being measured
Attach a ruler to clamp so it is vertical and parallel to the object being tested
Attach weights to the object being measured and use a fiducial marker or a set square to read ruler
What is a fiducial marker?
A pin of sorts which is hung on the bottom of a weight which allows measurements of distance to be taken more accurately
Describe ways in which measurements of extension can be taken more accurately
using a fiducial marker or a set square at eye level
Describe a method to find a spring constant of a spring, include how you would improve accuracy of your measurements
Measure original length of spring when no load is applied using a mm ruler clapped to a stand
Take readings at eye level using a fiducial marker to increase accuracy
Add lowest weight to the spring, once the spring is at rest record the new length of the spring
Use x=L-L0 to find extension
Measure mass of the weight using an electronic balance to, find weight by using mg
Repeat measurements at least 6 times with different weights
Plot a force extension graph using the results. Draw a line of best fit.
Gradient of the linear section is the force/spring constant
How to add spring constants for springs in series?
same as adding resistances in parallel (think inverse)
How to add spring constants for springs in parallel?
add them
How will the gradients of a single spring, two identical springs in series, and in parallel compare in gradients?
Take k as gradient for individual spring
Series will be 0.5k
Parallel will be 2k
Explain why the force constant will be given by 2k when two springs of force constant k are connected in parallel
F=kx
x is halved so k must double for same force
What does the area underneath a force extension graph?
(elastic potential) energy
Explain how the formula work done = 1/2kx^2
is derived?
Area under graph = 1/2Fx
F=kx
Plug this into the first equation
Explain why when using Fx to find elastic potential energy in a loaded spring, 1/2 must be used?
it’s an average - think a plot of these values, it’s not a square it’s a triangle on force extension graph
Why can the elastic energy stored in a spring not be directly linked to 1/2mv^2 in vertical motion?
GPE is not included
Three types of energy KE, EPE, GPE
