Two springs, with force constants k 1=150N/m and k 2=260N/m, are connected in se

Question

Two springs, with force constants k1=150N/m and k2=260N/m, are connected in series, as shown in (Figure 1).

When a mass m=0.50kg is attached to the springs, what is the amount of stretch, x?

Express your answer to two significant figures and include appropriate units.

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Explanation / Answer

Solution,

Force, F = kx

=> x = F/k

for spring 1, x1 = F/k1

for spring 2, x2 = F/k2

Resultant, x = x1 + x2

F/k = F/k1 + F/k2

1/k = 1/k1 + 1/k2

k = 95.12 N/m

x = F/k = mg/k = 0.50 x 9.8/95.12

x = 0.052 m = 5.2 cm

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