Question

5) The 4 kg collar Chas a velocity of 2 m/s when it is at A. If the guide rod is smooth, determine the speed of the collar when it is at B. The spring has an unstretched length of 0.2m. -k = 400 N/m А С 0.1 m ORAN 0.4 m B

Answer 1

I have applied energy conservation between point A and B.I assumed the reference(datum) at point B and calculated potenitial energy with respect to that point.

Hope it will help you.

solation A k= 400 Nm C 072 O D K 04m When the collars will be at B, the position of collos will be as shown in the given fig, A 0 1 701 0.3m DK 0.4m B of spring at 0.5m • longth at a B is given by, (0.3)2 + (0.4)² & Compresion in the spring is given by OC - = OC -- (unstoet- ched lough - OC -0.2 = 0.5-0.2 = 0.3m

between A and B, Apply Conservation of energy 1 muf+mgha + Lkx - 11 mv + mg h3 + 1 KK TA B VA = 2 mis V8 = ? hB =0 m = 4 kg HA = 0.4m Хе in spring XB = 0.5-0.2 = 0.3m Compression at A g=9.81 m/s² 2A = -> I have aesurmed datum at B, honce potential enogy will be zero at B. Now, petting all the value, (4xaxa) + (4x981 20:4) +( 4 x 400 x1043) = (4x4xV$) + (4x9:81x0) + (4 x400 x0:32) 8 + (16x9.81) + (200 X01 X01) + 0 + (200 x 033) 2V +0+ VE . = 1.962 mis