Question

Blocks A and B, with masses Ma= 5kg and Mb= 3kg, respectively, are connected by a spring of stiffness k= 20 N/m and unstretched length of 0.75m. The blocks are at rest and seperated by the distance 0.75m when block B is given a velocity to the rightwith magnitude v0=15m/s. The friction between blocks and the horizontal surface on which they rest is negligible.

The picture given looks like: [A]---------[B] where the dashed line is the spring.

Determing the maxium vlue of the distance d beween A and B that will be achieved during the motion.

Answer 1

IT wILL BE MAX . WHEN RELATIVE VELOCITY OF BLOCKS = O

vel of c.o.m = 15*3/8

= 5.625

relative velocity will b same when ther vel = vel of c.o.m

now energy conservation

1/2*3 * 15*15 = 1/2 * (3+5) * 5.625*5.625 + 1/2 * 20 x^2

x =4.592

d = 4.592 + 0.75

5.342 m