Question

The cylinder has a mass of 80 kg and is released from rest when h = 0. Each spring has a stiffness k = 30 N/m and an unstretched length of 2 m. (Figure 1) Part A Determine the cylinder's speed when h= 3.5 m. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) li μΑ ? Value Units Submit < Return to Assignment Provide Feedback igure 1 of 1 2 m 2 m K 4

Answer 1

Ans 2 umus x V the .. stretched suppose cylinder has moved below by xe length of spring :. stretch in spoing - Stretched length - original length z! Y+01² - 2 = √2²+x² 4 + x12 1 1 FBD 0 of cylinder, ka KX' o where, coso = R ſutre Vng mg-3kx'coso = > mg-ak Cu+22-2) Vu+n2 x ma = mg 2K x 2X t Vy+0² Putting 80 kg g - 10 mis² K = 30 N/m & dv da we get

60 2 Ź 800 - 2x √4+x22 80 udv dx h=3.5 =>1/800 60 x 120X ) de = 80 (var 4+22 du. 나 integration of (2ox wot 4+x2 I a 120X dn 4+02 let, 4 + x²=t => 2 adu - at => I = 60 dt 120 € VE = 120 4 +22 3.5 800 x - Gox² 120 4 +1² 80/12 2 2 => S00x3.5 - 3013:5)? + 120,54+3.52 -0+0-12054 = 400 40 v² => 2800 367.5 + 483:735-240 2676 235 = 40v? 2 > v² 66.906 -> N 8.179 m/sec A