How High Was the Plunger Released to Compress the Springs?

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The discussion centers on calculating the height from which an 8-kg plunger is released, using the principles of potential energy and spring compression. The outer spring has a constant of k1 = 3 kN/m and the inner spring k2 = 10 kN/m, with a maximum deflection of 150 mm observed in the outer spring. The equation mgh = 0.5kx^2 is applied to relate the gravitational potential energy to the spring potential energy. The derived height h is calculated to be 0.509 m, although there is a noted typo in the spring constant that prevents final confirmation of the answer. The calculations appear correct, but the discrepancy in spring constants raises questions about the accuracy of the results.
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1. An 8-kg plunger is released from rest in the position shown and is stopped by the two nested springs; the constant of the outer spring is k1 = 3kN/m and the constant of the inner spring is k2 = 1-kN/m. If the maximum deflection of the outer spring is observed to be 150mm, determine the height h from which the plunger was released.
Given a diagram. h is the height above the tallest spring, the outer spring. The outer spring is 90 mm higher than the inner spring.



2. mgh=PE .5kx^2=PE spring



3. mg(h+.15m) = .5k1(.15m^2) + .5k2(.06m^2)
Yielding an h of 0.509m.
Can someone inform me if this is the right path? It seems too simple...
 
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Theres a typo in your spring constant so can't confirm answer but work looks fine.
 
sorry, k1=3kN/m and k2=10kN/m if I remember correctly. Thanks for the confirmation.
 

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