InterviewSolution
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InterviewSolution
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A1.2 kg collar C may slide without friction along a fixed smooth horizontal rod. It isattached to three springs each of constant K 400 N/m and 150 mm undeformedlength. Knowing that the collar is released from rest in the position shown. Deteminethe maximum velocity it will reach in its motion. [Here A, O, B are fixed points.]ĺĽ |
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Answer» First find the deformed length of the springs. Spring 3: l = √((.15m)2 + (.3m)2) l = 0.3354 m Δx3 = 0.3354m - 0.15m Δx3 = 0.1854m Spring 2: l = √((.15m)2 + (.15m)2) l = 0.21213 m Δx2 = 0.21213m - 0.15m Δx2 = 0.06213m Spring 1: Undeformed Δx = 0m Now, Ei = PE (from the deformed springs, no KE or U) Ei = 1/2k1(Δx1)1 + 1/2k2(Δx2)2 + 1/2k3(Δx3)3 Ei = 1/2(400N/m)(0m)2 + 1/2(400N/m)(0.06213m)2 + 1/2(400N/m)(0.1854m)2 Ei = 7.6459J From the Law of Conservation of Energy Ei = Ef and velocity will be max when there is no spring potential energy restricting the collar and only KE. Ef = 1/2mv2 7.6459J = 1/2(1.2kg)v2 3.57 m/s = v |
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