Yahoo Answers: Answers and Comments for A vertical spring (ignore its mass), whose spring stiffness constant is 900 N/m, is attached to a table and is compressed down 0.170 m.? [Physics]
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From Jace
enUS
Wed, 13 Jan 2016 13:36:11 +0000
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Yahoo Answers: Answers and Comments for A vertical spring (ignore its mass), whose spring stiffness constant is 900 N/m, is attached to a table and is compressed down 0.170 m.? [Physics]
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From Jim: SPE = 1/2kx² = (0.5)(900)(0.170)² = 13.005 J
1...
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Wed, 13 Jan 2016 13:57:09 +0000
SPE = 1/2kx² = (0.5)(900)(0.170)² = 13.005 J
13.005 = KE = 1/2mV² = (0.5)(0.600)V² = 0.300V²
V² = 43.35
V = 6.58 m/s ANS (a)
time to reach max height = t = V/g = 6.58/9.81 = 0.67116 s
max height above top of uncompressed spring = h = 1/2gt² = (0.5)(9.81)(0.67116)² = 2.209 m
max height above top of compressed spring = h + 0.170 = 2.209 + 0.170 = 2.38 m ANS (b)

From electron1: Let’s use the following equation to determine ...
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Wed, 13 Jan 2016 14:13:58 +0000
Let’s use the following equation to determine the work that is done by the spring.
Work = ½ * k * d^2 = ½ * 900 * 0.170^2 = 13.005 N * m
As the spring expands 0.170 meter, the ball moves upward 0.170 meters. As this happens, its potential and kinetic energy increase.
∆ PE = 0.6 * 0.17 = 0.102 J
∆ KE = 13.005 – 0.102 = 12.903 J
½ * 0.6 * v^2 = 0.3 * v^2
0.3 * v^2 = 12.903
v^2 = 43.01
v = √43.01
This is approximately 6.56 m/s. As the ball rises to its maximum height, its velocity will decrease from 6.56 m/s to 0 m/s at the rate of 9.8 m/s each second. Use the following equation to determine this distance.
vf^2 = vi^2 + 2 * a * d
0 = 43.01 + 2 * 9.8 * d
19.6 * d = 43.01
d = 43.01 ÷ 19.6
This is approximately 2.19 meters. To determine its height above its original position, add 0.17 meter.