A New Principle of Equilibrium by Lewis G.N.

By Lewis G.N.

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So, if we can determine the amount of kinetic energy possessed by the block at point w, we can derive the required velocity vw. To find the kinetic energy at point w, we can apply the law of conservation of energy at points z and w as shown below: Let total energy at point z = Ez-total Then, Ez-total = Ez-kinetic + Ez-potential Ez-total = 1/2 . (m/gc) . vz2 + m . (g/gc) . hz Eq. 1-36 Ez-total = 1/2 . {(17,342 lbm/(32 lbm-ft/lbf-s2)} . 92 ft/s)2 + (17,342 bm) . (32 ft/s2/32 lbm-ft/lbf-s2) . 56 ft) ∴ Ez-total = 120,282 ft-lbf The energy lost in the work performed against friction, during the block’s Introduction to Energy, Heat, and Thermodynamics 27 travel from z to w, is accounted for as follows: W f- wz = Work performed against friction = (Dist.

2 m) ∴ Ez-total = 162,848 J The energy lost in the work performed against friction, during the block’s travel from z to w, is accounted for as follows: W f- wz = Work performed against friction = (Dist. w-z) . (Ff) = (50 m) . ” ∴ Ew-total = 1/2 . m. vw2 Or, vw = {2 . (Ew-total)/m}1/2 = {2 . 03 m/s b) Employing the law of energy conservation and principles of energy conversion, calculate the value of the spring constant for the shock absorbing spring system. Solution Strategy: The unknown constant k is embedded in the formula for the potential energy stored in the spring after it has been fully compressed, upon stopping of the block.

Vw2 Eq. 1-37 Or, vw = {2 . (gc) . (Ew-total)/m}1/2 = {2 . (32 lbm-ft/lbf-s2) . 74 ft/s b) Employing the law of energy conservation and principles of energy conversion, calculate the value of the spring constant for the shock absorbing spring system. Solution Strategy: The unknown constant k is embedded in the formula for the potential energy stored in the spring after it has been fully compressed, upon stopping of the block. , W spring = 1/2 . k . x2. So, if we can determine the amount of work performed on the spring, during the compression of the spring, we can derive the required value of k.

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