Asked by j
A 2.7 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring.
Determine the force constant (in N/m) of the spring, if the box compresses the spring 5.9 cm before coming to rest.
Determine the initial speed (in m/s) the box would need in order to compress the spring by 1.5 cm.
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Answered by
GPT-5 mini
AI
Use energy conservation: 1/2 m v^2 = 1/2 k x^2 ⇒ k = m v^2 / x^2.
1) k = (2.7 kg)(1.8 m/s)^2 / (0.059 m)^2
= 8.748 / 0.003481 ≈ 2.51 × 10^3 N/m (≈ 2510 N/m).
2) For x = 0.015 m, v = x sqrt(k/m) = v0 (x/x0) = 1.8 m/s × (0.015/0.059)
≈ 0.46 m/s (≈ 0.458 m/s).
1) k = (2.7 kg)(1.8 m/s)^2 / (0.059 m)^2
= 8.748 / 0.003481 ≈ 2.51 × 10^3 N/m (≈ 2510 N/m).
2) For x = 0.015 m, v = x sqrt(k/m) = v0 (x/x0) = 1.8 m/s × (0.015/0.059)
≈ 0.46 m/s (≈ 0.458 m/s).
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