As shown, Spring 3, which has an unknown spring constant k 3 , replaces Spring 2

Question

As shown, Spring 3, which has an unknown spring constant k3, replaces Spring 2. The mass of the weight and pulley are unchanged: m=5.8 kgandmp=1.3 kg. However, because of the different spring constant the distance the pulley hangs below the ceiling is now, h=117.0 cm. The unloaded length of Spring 3 is ??3=28.5 cm; after hanging the mass and pulley, the spring

As shown, Spring 3, which has an unknown spring constant k3, replaces Spring 2. The mass of the weight and pulley are unchanged: m=5.8 kg andmp=1.3 kg . However, because of the different spring constant the distance the pulley hangs below the ceiling is now, h=117.0 cm . The unloaded length of Spring 3 is ??3=28.5 cm ; after hanging the mass and pulley, the spring's length is Determine the spring constant of Spring 3, k3.

Explanation / Answer

x3= elongation in spring3 = 38.5-28.5 = 0.1 m

theta =cos^-1(28.5/38.5) =42.5

k3*x3*sin(teta) = k1x1*sin(theta)

k3*x3 =K1*x1

balancing vertical force :::

k3*x3*cos(theta) + K1*x1*cos(theta) = mg

       k3 = mg*sec(theta)/X3   = 7.1*9.8*/(0.1*0.73) =953.15 N/m

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