find the work done in stretching a spring of natural length 8cm from 10cm to 13cm. assume a force of 6N is needed to hold it a length of 11cm.
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Expert's answer
2013-03-27T09:15:35-0400
find the work done in stretching a spring of natural length 8cmfrom 10cm to 13cm. assume a force of 6N is needed to hold it a length of 11cm. Hooke's law:F = k*Δl k - stiffness Δl = l - l0, l0 - naturallength, l - length after stretching. In our case: 6 H =k*(11cm - 8cm) => k = 6H/3cm = 2H/cm Energy of deformationequals: E = k*(l-l0)^2/2 The law of conservationof energy: E1 + A = E2 A - the work donein stretching a spring E1 = k*(l1 - l0)^2/2, E2 = k*(l2 - l0)^2/2 l1 = 10 cm, l2 = 13 cm Finally: A = k*(l2 - l0)^2/2 - k*(l1 - l0)^2/2 = 2 H/cm*(13cm - 8cm)^2/2 - 2 H/cm*(10cm - 8cm)^2/2 = 5^2 H*cm - 2^2 H*cm = 21 H*cm = 0.21 H*m = 0.21 J Answer: the workdone in stretching a spring equals 0.21 J
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