Motion with constraints concept

Motion with constraints are restrictions applied on the movement of body by various method or in other language motion confined body have to move in the confined direction brought by constraint forces  for example we may restrict the body to move along a straight wire see an example below picture. Above first picture shows that two block are connected with string which is not stretchable if block A moves with speed 5m/s then block B will also move with velocity 5m/s because of connected with string hence same velocity for both the block while in second case where A moves with velocity 2m/s then as shown arrangement what will be velocity of block B ? as block A moves block B will moves on ground horizontally not in air along attached string but string is common for both the block hence string velocity will be 2m/s hence we have to take component of horizontal velocity Vb along string because this string is causing motion for block along horizontal so take component Vbcos37  = 2 or Vb = 2/cos37  = 10/4 = 2.5m/s hence velocity of block B along horizontal Vb = 2.5m/s. velocity of any two point along the string must be same otherwise string will break so for common string velocity is same for every point.
below given example of constraints motion.

from the above first Q1 we have to find Va the actual movement of A will be horizontal towards right hence take a component of Va along string velocity so Vacos37  = 2 or Va = 10/4  = 2.5m/s hence Va = 2.5m/s towards right.
in second Q2 Velocity of block A is 5m/s towards left now take a component of 5m/s along string velocity along string = 5cos37 = 4m/s now this string is common for block B so same velocity of block B along string that is 4m/s now take a component of Vb along string Vbcos53  = 4 0r Vb = 20/3m/s.
now take example for pulley cases.

now from the above question we have to find velocity of block c for this start from pulley P2 we know that general formula for P2 pully  va+vb  = 2p2 here vb =0 so  0+4 = 2p2 or P2 = 4/2 = 2 m/s  direction is below hence P2 is moving with velocity 2m/s down hence P3 will move with 2m/s up hence apply now formula at P3 pulley  vb+vc  = 2*2 here vb = 3m/s put in this equation
3+vc = 4 vc = 4-3  = 1 m/s hence vc = 1m/s.
now you can solve more question using this concept i hope you have enjoyed   Motion with constraints concept thanks for reading
dated 5th Aug 2018