PHYS 17200 Lecture Notes - Lecture 6: Modulus Guitars, Friction, Proper Length
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PHYS 17200 - Modern Mechanics - Lecture 6_Ball-Spring Model of Solids
Contact Interactions and A Model of Solid Materials
● An atom is a neutral system consisting of a positively charged nucleus and a
negatively charged “cloud” of electrons that surrounds it. Typically, the spherical
cloud has a radius of about 10^-10 m, the size of the atom.
● The forces atoms exert on each other are fundamentally electrical, both nuclei
interacting with all the electrons and each other, but a simple fact makes it easy
to model the forces atoms exert on each other when they are bound into a single
molecule or into macroscopic arrays in a solid material.
● When a little further apart than that they attract each other. When a little closer
than that they repel each other. For small changes in their length chemical bonds
act like springs!
● Youngs Modulus
○ Strain = delta_L / L = change in length / rest length
○ Stress = F_spring / A = force exerted on wire / cross-sectional area of
○ Y = stress / strain
○ k_s_wire = (A / L) * Y = spring stiffness constant
● Interatomic Spring Stiffness: k_s_bond = Yd
○ k_s_bond = Stiffness of bond between each atom
○ d = distance between atoms
● When one object slides on another, the component of force exerted by one object on the
other has a component parallel (or antiparallel) to the motion:
○ | f | ~ k|FN|, magnitude of friction force
○ k is the coefficient of kinetic friction
○ s is the coefficient of staticfriction
○ FN is the “normal force” – the perpendicular component of the force that is
squeezing the two objects into each other
● If F_applied <k*FN ?
○ If it is moving, the block slows down.
○ If it is at rest, it stays at rest.
● If s > k
○ After the block stops it takes a larger force to get it moving again that it does to
keep it moving.