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Yo=[ 1 cm. Yo = [ Hooke's law. K= F/Ly HOT Mass | Face=ma Ay=Y-Yo mi F = mg AY,= Y, - % 509 100 7 10.6m doi To determine the soring of Une 우 Y lligam & ginen spring by Verifying Constant AY جرررد 150 4 F = mig 200 M2 Hooke's law F = KAY F2 = m29 250 300 Kar=[ Draw a graph of F Vs AY Find the slope RISE - K RISE Slovee- 2 RUN Run % dig AY 1 1 4 1 TL EXPERIMENT Simple Harmonic Motion TI EQUIPMENT NEEDED • Coil spring • Wide rubber band • Slotted weights and weight hanger • Laboratory timer or stopwatch • Meter stick Laboratory balance • 2 sheets of Cartesian graph paper The objective: to detrmine the spring TI THEORY F = ky A. Hooke's Law Ya The fact that for many elastic substances the restor- ing force that resists the deformation is directly pro- portional to the deformation was first demonstrated by Robert Hooke (1635–1703), an English physicist and contemporary of Isaac Newton. For one dimension, this relationship, known as Hooke's law, is expressed math- ematically as Quie llelele y Slope = k Y2 2m F = -Ar = -k(x - x) (TI 14.1) Elastic limit or Breaking point Y TI Figure 14.1 Hooke's law. An illustration in graphical form of spring elongation versus force. The greater the force, the greater the elongation, F = -ky. This Hooke's law relationship holds up to the elastic limit. F = -x (with x, = 0) where Ar is the linear deformation or displacement of the spring and x, is its initial position. The minus sign indicates that the force and displacement are in opposite directions. For coil springs, the constant k, is called the spring or force constant. The spring constant is sometimes called the “stiffness constant," because it gives an indication of the relative stiffness of a spring--the greater the k, the greater the stiffness. As can be seen from TI Eq. 14.1, k has units of N/m or lb/in. According to Hooke's law, the elongation of a spring is directly proportional to the magnitude of the stretching force.* For example, as illustrated in • TI Fig. 14.1, if a spring has an initial length yo, and a suspended weight of mass m stretches the spring to a length Yı, then in equilib- rium the weight force is balanced by the spring force and F = mg = kly1 - y.) F = 2mg = k(y2 - y) and so on for more added weights. The linear relation- ship of Hooke's law holds, provided that the deformation or elongation is not too great. Beyond the elastic limit, a spring is permanently deformed and eventually breaks with increasing force. Notice that Hooke's law has the form of an equation for a straight line: F = kly - Yo) Here y is used to indicate the vertical direction, instead of x as in TI Eq. 14.1, which is usually used to mean the hori- zontal direction. Similarly, if another mass m is added and the spring is stretched to a length v2, then or F = ky - ky which is of the general form y = x + b *The restoring spring force and the stretching force are equal in magnitude and opposite in direction (Newton's third law). 223 Copyright © Brooks/Cole. All rights reserved. Hooke's LAW -F=KAY obj: To determine the spring fonetart of the green specing lly verifying Hoove's Law Draw a graph of Fussy F Brixe slope ayl slope rise -K run run -KAY V Spring Constant m F = mg BY % diff Yo=[ K=E AY y 10.6 k=N 在 11.8 m AY, [m2 = m2 g Fomg JY,=Y-Yo 11.8-10.6 = 12cm Yo=[ ]cm mass FENCE-ing Aye y-yo K= Flay (%) BY =Y-Yo im F = mig 50 100 150 200 250 300 Kaug & [ Yo=18cm 50 21cm 100 25cm 130 28cm 200 31.5cm 250 35cm 300 38
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