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/mand 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.)(Figure 1)

Part A

bottom spring:

Part B

middle spring:

Part C

top spring:

l1 =   m   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/mand 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.)(Figure 1) Part A bottom spring: l1 = m Part B middle spring: l2 = m Part C top spring: l3 = m

Explanation / Answer

For bottom spring, mass hung is 3.4 kg. So,

F = mg = 3.4 * 9.8 = 33.32 N.

Also, F = kx

33.32 = 5700 * X

X = 5.85 mm.

Middle spring-

M = 3.4 + 3.4 = 6.8 kg

F = 6.8 * 9.8 = 66.64 N

F = kX

X = 66.64 / 5700 = 11.69 mm.

Top spring-

M = 3.4 + 3.4 + 3.4 = 10.2 kg

F = 133.28 N

X = 23.38 mm.

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