Asked by ABAINEH
14.A 1kg block is dropped from a height h above the top end of a vertical spring with k=1200N/m. If the block compresses the spring by 0.1m and momentarily comes to rest, what is the height from which the block was dropped? A.0.2m B. 0.4m C.0.3m D.0.5m
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Use energy conservation (neglecting losses). The block falls a total distance h + x, so
m g (h + x) = 1/2 k x^2.
Solve for h:
h = (k x^2)/(2 m g) - x.
Plugging in m = 1 kg, k = 1200 N/m, x = 0.1 m, g ≈ 9.8 m/s^2:
(1/2)k x^2 = 6 J, so h + x = 6/9.8 ≈ 0.612 m,
h ≈ 0.612 − 0.1 = 0.512 m ≈ 0.5 m.
Answer: D (0.5 m).
m g (h + x) = 1/2 k x^2.
Solve for h:
h = (k x^2)/(2 m g) - x.
Plugging in m = 1 kg, k = 1200 N/m, x = 0.1 m, g ≈ 9.8 m/s^2:
(1/2)k x^2 = 6 J, so h + x = 6/9.8 ≈ 0.612 m,
h ≈ 0.612 − 0.1 = 0.512 m ≈ 0.5 m.
Answer: D (0.5 m).
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