Conservation of momentum in pulley

[jd12345]

Two blocks of mass m connected by a light string passing over a pulley.
Say, one of the blocks is pushed downwards with a force F and it attains velocity v.So the other block moves upwards with the same speed v right?

Total moementum = mv - mv = 0( because one is moving upwards and other downwards so opposite directions of velocity)

So we applied force but still no momentum change??
Where did i go wrong??

 

[Doc Al]

Momentum is a vector, for one thing. Direction counts. And do not ignore the external force of the pulley's axle on the system.

 

[Rap]

Two blocks of mass m connected by a light string passing over a pulley.
Say, one of the blocks is pushed downwards with a force F and it attains velocity v.So the other block moves upwards with the same speed v right?

Total moementum = mv - mv = 0( because one is moving upwards and other downwards so opposite directions of velocity)

So we applied force but still no momentum change??
Where did i go wrong??

When you push on the one mass, you are also pushing on the pulley, and the pulley is connected to the earth, so you are pushing on the Earth too. Momentum is only conserved for the whole system, not its pieces. The pieces are the two masses, you, and the pulley-earth (they are rigidly connected). The force that you apply adds momentum to the earth, not to the masses.

When you push on the mass, it pushes back (Newton's law). That means you have momentum up, which matches the down momentum of the pulley-earth. Total momentum is still zero. When you stop applying the force, gravity pulls you and the pulley Earth together, and both stop. The masses are moving with zero momentum, you and the pulley Earth are motionless, and again, total momentum is zero.