Question

The vent plate is supported at B by a pin. It weighs m= 54 N and has a center of gravity at G.

0.15 m B \0.3 m -1.2 m

Determine the stiffness k of the spring so that the plate remains in equilibrium at θ= 30 deg. The spring is unstretched when  θ= 0 deg (express your answer with the appropriate units).

k=

Answer 1

0.3m 03 38 03 Sino free body diagram The system has only one degree of freedom defined by the independent co-ordinati o. When 0 undergoes a positive displacement Se. Virtead displacements the weight of the vent plate Sqw force) * located from fired point B using the position co-ordinate G. The horizontal and vertical position of the spring face to measured from the fired point B using the position co-ordinates to and Ya, respectively Y = 0-15 COSE SY -045 Sine so YA = 0-3 COSE SY = -03 Sino se 1403 Sine 52 = 0 3 0 0 S 0 virtual work equation when I YA and an undergo positive virtual displacements S4G, SUA and as the weight of the vent plate 1 5(w force), horizontal plate component of fp, tip case and Ventical component of the sind do negative work. Su=0; -Esp cos & 87 - Sp sind 54 - 59 8460

-Cop Cosa cod 8.3) - sest (-0.3 sino. 8) -54 Co.15 sino So): 800 - - 0.3) Ojo cose + tse s'n. Stre03) +54 (0.15)sine =0 fp cos (+) .03) + 8.1 Sino 20 . 27 sene Solismo 0-3 cos (+) cos (+) al equilibmium position 0-38, the angle $ - Tan ( 0.360836 1.2 + 0.38638 10.89 21 Sino of = 27 88n38 COS 30+10.89 - 17.65 N COS (+0) from the geometry 1. | spring stretches 4 0 - - 1) (0-3) Cosas - - - - = 6.137 m. Esp = kx k= £ / 4 = 17.85 - 130.29 N/m 0.137 K 1-3 KNM
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