I dont know what i did wrong i got 91.4 N/m for the spring constant Finding the

Question

I dont know what i did wrong i got 91.4 N/m for the spring constant

Finding the spring constant As shown, Spring 3, which has an unknown spring constant k3, replaces Spring 2. The mass of the weight and pulley are unchanged m = 4.5 kg and mp = 1.0 kg. However, because of the different spring constant the distance the pulley hangs below the ceiling is now, h = 116.0 cm. The unloaded length of Spring 3 is = 25.5 cm; after hanging the mass and pulley, the spring's length is ell3 = 35.5 cm. Determine the spring constant of Spring 3, k3. Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

k3*x3*cos(theta) +k1*x1*cos(theta) = (m+mp)g

and k3*x3*sin theta = k1*x1*sin theta

==> k1*x1 =k3*x3

so, 2*k3*x3*costheta = (m+mp)g

==> k3 = (m+mp)g/(2*x3*cos(theta ))

here, x3 = l3-l'3 = 35.5-25.5 = 10 cm

cos theta = h/l3 = 116/35.5 =3.27

so k3 = (4.5+1)*9.8/((2*10*10^-2*3.27)

=82.4

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