A 1.0 kg block attached to a horizontal spring oscillates with simple harmonic motion. When its displacement is x = 0.05 m, its speed is v = 0.2 m/s, and when x = 0.08 m, its speed is v = 0.1 m/s. What is the spring constant k?
Answer and explanation
Correct answer: B. 7.69 N/m
- Step 1: Total energy E = (1/2)kx^2 + (1/2)mv^2 is conserved.
- Step 2: Therefore (1/2)k(0.08^2 - 0.05^2) = (1/2)m(0.2^2 - 0.1^2).
- Step 3: k (0.0064 - 0.0025) = 1.0 (0.04 - 0.01).
- Step 4: k * (0.0039) = 0.03, so k = 0.03 / 0.0039 = 7.692 N/m.
Answer
7.69 N/m.
Why not the others: 10.0 N/m is an estimate; 5.25 N/m calculates using a single point assuming amplitude 0.1 m; 12.5 N/m uses m = 1.6 kg.
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