Three identical 3.40kg masses are hung by three identical springs, as shown in t

Question

Three identical 3.40kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 5.70kN/m and was 19.0cm long 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.)

Part A

bottom spring:

Part B

middle spring:

Part C

top spring:

l1 =   m   hree identical 3.40kg masses are hung by three identical springs, as shown in the figure. Each spring has a force constant of 5.70kN/m and was 19.0cm long 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.) Part A bottom spring: l1 = m Part B middle spring: l2 = m Part C top spring: l3 = m

Explanation / Answer

If X is the extension of each spring

3.40 * 9.81 = 5.70 * 10^3 * X

X = 5.851*10^-3 meters

the length of each spring is therefore

0.19 + 0.005851 = 0.195 m

therfore l1 = l2 =l3 = 0.195 m

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