Maximum distance spring compressed.

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To find the maximum distance the spring is compressed when a block is dropped onto it, the equation mgh = 1/2kx^2 is used, where m is the mass, g is gravity, h is the height, k is the spring constant, and x is the compression distance. The initial calculation of x = 0.138m is incorrect because it does not account for the additional distance the block travels while compressing the spring. The gravitational force continues to act on the block during compression, meaning the total distance must include both the drop height and the compression distance. To solve correctly, the energy balance must consider the total potential energy converted into spring potential energy. The correct approach requires adjusting the height in the potential energy equation to reflect the total distance the block falls.
AnnieD
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A block of mass m = 1.9 kg is dropped from height h = 77 cm onto a spring of spring constant k = 1510 N/m (Fig. 8-38). Find the maximum distance the spring is compressed.

My attempt:
mgh = 1/2kx^2
(1.9)(9.8)(.77) = (.5)(1510)x^2
x = 0.138m

But it's not the correct answer.
What am I doing wrong?
 
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gravity is still working on the block when it is compressing the spring

by writing h in your potential energy, you are saying that h is the distance onlong which the block "feels" gravity

you are going to need to add something there...

marlon
 
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