Consider a spring with a force constant of 965 N/m. Suppose the mass of the block is 1.70 kg, but its initial speed can be varied. What initial speed is required to give a maximum spring compression of 3.70 cm.
Question
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Answer: 0.88 m/s
Explanation:
given
Force constant of the spring, k = 965 N/m
Compression of the spring, x = 3.7 cm = 0.037m
Mass of the block, m = 1.7 kg
To solve this, we would be using law of conservation of energy, where initial energy is all kinetic and elastic energy is elastic but potential.
E(f) = E(i)
1/2kx² = 1/2mv²
kx² = mv²
965 * 0.037² = 1.7 * v²
1.321 = 1.7 v²
v² = 1.321 / 1.7
v² = 0.777
v = 0.88 m/s
Thus, the initial speed of the block is v = 0.88 m/s