Your boss hands you a bag containing four springs, A, B, C, and D, and tells you that they all have the same relaxed length. He wants you to rank them by the values of their spring constants. He locks you in a room with only the springs, a ruler, and a pad and pencil, and tells you to knock when you're done. Each spring has a hook on one end and a handgrip on the other. There is nothing in the room you can use to measure inertia.

After thinking for a few minutes, you hook springs A and B together, stand on one handgrip with your foot, and pull on the other handgrip with your hand until the combination spring has been stretched to double its original length (Figure P8.58). You notice that spring A makes up \(65 \%\) of the stretched length and spring B makes up the other \(35 \%\).

Data from Figure P8.58

You work your way through the rest of the springs and tabulate the results:

Based on these results, what are the numerical values in the ratio \(k_{\mathrm{A}}: k_{\mathrm{B}}: k_{\mathrm{C}}: k_{\mathrm{D}}\) ?

Transcribed Image Text:

wwwwwwwww 65% 35% B