Hooke's Law
Research Instroduction
Firstly The elastic properties of matter are involved in many many physical phenomena. When matter is deformed (compressed, twisted, stretched, et cetera) and the deforming forces are sufficiently small, the material will return to its original shape when the deforming forces are removed. In such cases, the deformation deformation is said to take place within the elastic limit of the material, i.e., there is no permanent deformation. The slight stretching of a rubber band is an eample of an elastic deformation. !teel wires, concrete columns, metal beams and rods and other material ob"ects can also undergo elastic deformations. For many materials, it is approimately true that when the material is stretched or compressed, the resisting or restoring force that tends to return the material to its original shape is proportional to the amount of the deformation but points in a direction opposite to the stretch or compression. This This ideali#ed behavior of matter is called $ooke%s &aw. Today's Today's lab will allow you to test the accuracy of $ooke's law for a simple ob"ect, a spring.
Simplified Theory
The Hooke’s Law theory is the statement that the restoring force acting on an object is proportional to the negative of the displacement (deformation) of the object. In symbols
! " #k$
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The meaning of (!) is the restoring force provided by whatever is being stretched (or s%&ee'ed)
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The meaning of ($) is the displacement of the thing being stretched (or s%&ee'ed).
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The meaning of (k) is the constant of proportionality.
The negative sign (#) is important and j&st says that the restoring force is opposite in direction to the displacement. !or e$ample if a spring is stretched by something in a certain direction the spring will e$ert a restoring force on that something b&t in the opposite direction. %&ation also says that for an object which obeys Hooke’s law (s&ch as a spring) the more it is stretched or s%&ee'ed the greater will be the restoring force s&pplied by the object on whatever is doing the stretching or the s%&ee'ing. *n applied force (!) acting on o&r +Hookean, object will ca&se it to be displaced (stretched or s%&ee'ed) by some amo&nt ($). The ratio of the change in applied force and the change in the res<ing displacement is called the spring constant (k) and can be written as follows- ( k " )
Today’s e$periment will test this relationship for a large spring. y hanging different masses from the spring we can control the amo&nt of force acting on it. /e can then meas&re for each applied weight the amo&nt that the spring 0stretches., 1ince %&ation () is the e%&ation for a straight line a graph of ! (the weight) vers&s $ (the 0stretch0) will sho&ld yield a line with slope k . %&ation (2) tells &s the same thing and its appearance sho&ld remind yo& of how to comp&te the slope of a straight line.
Procedure ( Method )
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Install a table rod with a rod clamp near its top. !uspend a helical spring from the clamp with the large end up.
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ttach a * g weight hook with a * g slot mass on it to the spring. +ecord the initial mass of ** g as m . The parameter m will represent the total mass on the spring.
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-lace the meter stick vertically alongside the hanging mass. easure the elongation of the spring and record it as . lways be sure to measure starting at the same place, either on the table or on the clamp.
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dd a * g slot mass to the hook and record m/ (* g). +ead the meter stick and record /. +epeat, finding 0 , 1 , , and 2 with total masses /** g, /* g, 0** g, and 0* g. +ecord all the masses and elongations on the form provided.
hart!
"st Measurement of $nd Measurement %rd Measurement Stretchin#(cm) of Stretchin#(cm) of Stretchin#(cm) &#(" uncertainty) & "#(" uncertainty) "% "" "$ "&#($ uncertainty) $ "* " The uncertainty +alues a,o+e were found ,y the formula of (ma-.min)/$ 0+era#ed(processed) +alues ta,le! Sprin# Stretchin# 0mount(cm) &# load " # load "$ "& # load "*
Graph ( Logger Pro ):