A 1.70 kg object is held 1.20 m above a relaxed massless spring with a spring co

Question

A 1.70 kg object is held 1.20 m above a relaxed massless spring with a spring constant of 340 N/m. The object is dropped onto the spring. (a) How far does it compress the spring? m (b) How far does it compress the spring if the same experiment is performed on the moon, where g = 1.63 m/s2? m (c) Repeat part (a), but this time assume a constant air-resistance force of 0.700 N acts on the mass during its motion. m

Explanation / Answer

a) m * g(h+x) = 1/2 * k *x^2 1.7*9.81(1.2+x) = 1/2 * 340 * x^2 => 170X^2 - 16.677x-20=0 => x= 0.3955. b) 1.7*1.63(1.2+x) = 1/2 * 340 * x^2 => 3.3252+2.771x=170x^2 => 170x^2-2.771x-3.3252=0 x= 0.148 c) m * g(h+x) = 1/2 * k *x^2 + 0.7(h+x) => 15.977(1.2+x) = 170 x^2 => 170x^2-15.977x-19.172=0 =>x=0.386

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