Question

The figure (Please see the figure on page 198) shows two different ways of combining a pair of identical springs, each with spring constant k. We refer to the top setup as parallel and the bottom one as a series arrangement. Instruction (a) For the parallel arrangement, 1. Draw a free body diagram and draw all the forces acting on the connector plece on the left. 2. write down the net force equation based on the free body diagram. 3. Using the fact the F-kx, determine the equivalent spring constant of the whole setup. Explain whether the combined spring constant should be interpreted as being stiffer or less stiff. (b) For the series arrangement, 1. Draw free body diagrams and draw all the forces acting on the connector piece on the left and the joint point of the two springs. 2. write down the net force equations based on the free body diagram 3. Using the fact the F-kx, determine the equivalent spring constant of the whole setup. Explain whether the combined spring constant should be interpreted as being stiffer or less stiff.

Answer 1

O for parallel Cambriation (6 (6) for series Combination kux *, numerür sf the latal stretching = x W x = With funds Kipr, 2721 Frut = -(k, x + H₂M) =-x (ki+H₂) Camparing with F=uka k=kitka Using Hoah's law F=kin, F = K2 U2 Querall spring constant will stiffer since the direct addition will increass the overall amount x=fltt x= f( 4th 2) F = / Killalox Thith, k = kilka kitka ich we take k, = 4₂=n K= 1x so not spring will kuam less stiffer

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