Hooke\'s law describes a certain light spring of unstretched length 33.0 cm. Whe

Question

Hooke's law describes a certain light spring of unstretched length 33.0 cm. When one end is attached to the top of a door frame and a 8.60-kg object is hung from the other end, the length of the spring is 46.5 cm.

The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 180 N. Find the length of the spring in this situation.

Explanation / Answer

Find its spring constant.>> Force = F = kx where F = load applied on the spring = mg m = mass of the load = 8.60 kg (given) g = acceleration due to gravity = 9.8 m/sec^2 (constant) k = spring constant x = change in length of the spring when a load is applied = 7 cm Substituting appropriate values, 8.60(9.8) = k(34/100) k = 8.60(9.8)(100)/7 k = 1.204 kN/m This situation is equivalent to a force of 300 N acting on one side of the spring (with the other side held fixed). This being said, then 300 = k(x) = 1204(x) x = 300/1204 x = 0.249 m x = 24.9 cm.

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