Three identical 9.40 masses are hung by three identical springs, as shown in the

Question

Three identical 9.40 masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 5.90 and was 16.0long before any masses were attached to it. How long is each spring when hanging as shown? (Hint: First isolate only the bottom mass. Then treat the bottom two masses as a system. Finally, treat all three masses as a system.)(Figure 1) Part A: What is bottom Spring in Meters Part B. What is middle spring in Meters. Part C: What is top spring in meters. Please explain step by step with solution included, thank you very much!

Explanation / Answer

Write the force balance at each mass point. For the bottom mass, the forces are the weight, m*g and the spring force from the bottom spring. If the bottom spring extends by ?x3, and the spring constant is k, that force is k*?x3. This gives the equatiion m3*g = k3*?x3 For the next higher mass, the force is (m2 + m3)*g and the spring force is k2*?x2 (m2 + m3)*g = k2*?x2 and for the highest mass (m1 + m2 + m3)*g = k1*?x1 You know all the masses, and the spring constants; they are all the same so the equations become m*g = k*?x3 2*m*g = k*?x2 3*m*g = k*?x1 There are 3 eq in 3 unknowns, solve for them. The lengths are initial length + ?x

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