A 700 gram block is released from a height h above an ideal spring of spring constant 400 N/m. The block sticks to the spring?

Question

A 700 gram block is released from a height h above an ideal spring of spring constant 400 N/m. The block sticks to the spring, and comes momentarily to rest after compressing the spring by an amount of 19 cm.

(a) What is the value of the initial height h?

i got 0.88 m but its wrong

(b) What is the height of the block when it again comes to rest momentarily--the block remains connected to the spring? Measure from the equilibrium position of the spring.

i got 0.17 m but it says its wrong

? · Accepted Answer

(a) At maximum spring compression, the block has fallen through
h + 0.19m

PE becomes SPE:
0.700kg * 9.8m/s² * (h + 0.19m) = ½ * 400N/m * (0.19m)²
6.86N * (h + 0.19m) = 7.22 J

h = 0.862 m

I think that to have marked "0.88 m" wrong is pretty picky.

(b) Now SPE in compression becomes SPE in tension and GPE:
7.22 J = ½ * 400N/m * x² + 6.86N * (x + 0.19m)

x = 0.156 m

Again, pretty close to your result.

Maybe they want the answers in cm?

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A 700 gram block is released from a height h above an ideal spring of spring constant 400 N/m. The block sticks to the spring?

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