Question

dynamics

A delicate 0.2 lb instrument is placed in a tray. To protect it during shipping it is attached to a spring as shown in the figure. Given the spring's experimentally obtained stiffness characteristics, shown below, what is the maximum velocity for the tray and instrument if the force on the delicate instrument is not to exceed 12 lbs. Assume the tray comes to an abrupt stop. The force can also be represented by the following interpolated polynomial function of x. FCx)= 3.135 -4.333x2 +5,33372-2.667 x4 +0.5333x5 F (16) 12 + 8 6 4 N Brin.)

Answer 1

Mass is given 0.2 lb

F(x) is given .

Force can not be exceed 12 lbs .

Find maximum velocity

f(x?= 3.133 * = 4.333 x?+5.33323-8.6673"40, 53333 5 f(x) = I2lbs. mux Now. eancate to 12 lbs. S 3.133x – 4.333 x?+5.3333 13_2.6672"+0.53333 on solving we get x=2.5o (: use graphical calculatos) 26=2.sol Now Elastic enesay = (fos.de 215 0 2.sol 13.1332-4.333x?+5.33343-2.65744 +0.53333) do 2.51 ما 11 S [241.392 3.1334?_4.3332 +5.3332?_ 2.667% papasaya'] 4 [.. 1.44932+ 1.3333 0.53342'* 0.0869] 2.500 5665x? 8.92 Joule. V

Hese K. E = Elastic enessy, Now max. speed is Vinar -1.m. (Vmax) 2 K.E 2 2 8.92 - [x 0.2 (Vmax) 2 :. Vmax = 9.4446 mis Have you understood the salation ? live letins