Springs, Young modulus Flashcards
Limit of proportionality
Up to this point the material obeys Hooke’s law. Extension is proportional to the force applied
How is Hooke’s law is shown on a force/extension graph?
Straight line through the origin
Elastic limit
The point after which the material will not return to it original shape when the force is removed
Plastic material
A material, which will not return to its original shape after the force is removed from it
Ultimate tensile strength
Maximum amount of stress that can be applied to a material without making it break
Breaking point
The point where material breaks
Breaking Stress
Stress applied to material that causes it to snap/break
Equation of breaking stress
Breaking stress = breaking force/(initial length * section area)
What happens to the spring constants of springs in series
Ktotal=K1+K2
What happens to the spring constants of springs in parallel
1/Ktotal=1/k+1/k
Equation linking force, extension and spring constant
F=ke or F=kx
Equation linking word done, force and extension
WD=1/2F*e
Britle
A material which snaps once enough stress is applied ie doesn’t bend
Ductile
A material that can be bent into a shape of a wire
Polymeric
A material that has a very large strain, but low stress
In an elastic band where does the energy lost go?
Friction between the molecules (heat)
Hysteresis
Area between the loading and the unloading part of the force/extension graph
Stress
Force per unit area
Strain
Change in length per original length
Stress equation
=F/A
Strain equation
=Extension/original length
Units of stress
Pa
Units of strain
No units
Young modulus equation
=Stress/Strain
What do tensile forces do?
Stretch the object
What do compressive forced do?
Squash the object
Hooke’s Law
The extension of a spring is directly proportional to the force applied until the elastic limit is exceeded
Why is energy stored in stretched springs
A force has been applied to the spring to move it through a distance → force has done work → WD=FD → force in spring =ke → WD proportional ke^2
Equation linking work done, spring constant and extension
W=1/2ke^2
Equation linking work done, spring constant and force
W=1/2 * (F^2)/k
Plastic deformation
When loading off a spring it doesn’t return to its original length as the elastic limit has been passed, permanent change in length
How to determine a Young Modulus of a wire? (5)
- Use a micrometer at several points to find the diameter, take the average
- Clamp the wire at one end and suspended taught using a pulley at the other end
- Place a ruler parallel to the wire with a fiducial marker placed so that the extension of the wire can be measured
- Apply different forces
- Plot a graph and calculate YM using the formula
