Hooke's Law

Hooke's Law

• States: The force(F) needed to extend or compress/extend a spring or elastic body by some distance x scales linearly with respect to that distance up to the limit of proportionality
• Symbolic: F∝x
• Equation: F=kx
• where k is the stiffness of the object = Nm-1
• SI units: kgms-2=k m
• Say a spring has stiffness constant k, and a weight of 1kg hanging off of it and due this moves distance x
• In series, this is 0.5k, 1kg and 2x
• In parallel, this is 2k, 1kg and 0.5x

Deformation

• Elastic
• Up to the limit of proportionality
• Material returns to original shape
• Tension = atoms pulled apart = moving slightly from equilibrium position, no tension = atoms return to equilibrium distances apart
• Plastic
• Beyond the limit of proportionality
• Material does not return to original shape
• Tension = atoms pulled apart = move position in material, no tension = atoms remaining in this position

Investigating extension

• Equipment: Clampstand, clamp, meter ruler, object, weights
• Clamp the object, measure its length and add weights one at a time to the bottom of the object
• After each weight, measure the new length and calculate extension = new length - original length
• Plot the graph of Force vs. extension
• Where the line is straight, Hooke's law is obeyed, therefore gradient = k
• If you load object with weight beyond the limit of proportionality, the line will curve down
• Safety: stand whilst performing to get out of the way if the object falls, safety goggles in case object snaps