## pratu043 3 years ago I have a doubt in the answer key to the problem on law of conservation of momentum. The question: A girl of mass 50 kg jumps out of a rowing boat of mass 300 kg on to the bank with a horizontal velocity of 3 m/s. With what velocity does the boat move backwards? Answer key says: m1(mass of girl) = 50 kg m2(mass of boat) = 300kg v1(velocity of girl) = 3 m/s v2 = ? m1v1 + m2v2 = 0 How can the momentum of the whole system after the girl jumps out of the boat be 0? The boat will have some momentum right?

1. Xishem

Right. The boat must have some change in velocity, since the momentum must be conserved and the momentum of the girl changed.

2. Yahoo!

it is just same as recoil velocity of Gun..

3. pratu043

but even in recoiling of gun, how can the final momentum be 0?

4. Yahoo!

v = - Mv/m = -50*3/300 = -0.5m/s

5. pratu043

Yes, I know the answer but I can't understand how total momentum is 0.

6. Yahoo!

Law of conservation of momentum..says that momentum is conserved

7. Yahoo!

Do..u knw abt Rocket propulsion

8. Xishem

Momenta are vectors.

9. Xishem

If you have two vectors in opposite directions, they can cancel eachother out.

10. Yahoo!

even though the mass gets reduced..the momentum is conserved

11. pratu043

even if they are different?

12. Xishem

The girl's momentum is in one direction and the boat's in another direction.

13. Yahoo!

yup..@Xishem has a point there

14. pratu043

I mean do they cancel each other even if the magnitudes are different?

15. Xishem

The magnitudes aren't different.

16. Xishem

Remember, momentum is a function of both mass and velocity.

17. Xishem

If one object with 1kg mass and 10m/s velocity is moving right and another of 10kg mass and 1m/s velocity is moving left, the total momentum is zero.

18. pratu043

So mass*velocity of the bullet or girl will always be equal to mass*velocity of gun or boat?

19. Xishem

Yes, assuming you are in a closed system. Which you are.

20. pratu043

What is a closed system?

21. pratu043

22. Xishem

A closed system is a physical system which doesn't exchange any matter in or out of itself and which isn't affected by outside forces.

23. Xishem

It basically just means that you are only considering the two objects and not nonconservative forces like friction which would change the overall momentum. (This case is frictionless, but that's one case where momentum won't be conserved).

24. pratu043

Thanks I got it now.

25. pratu043

This doesn't happen in the case of a collision right?

26. Xishem

Momentum is not conserved in an inelastic collision. Momentum is conserved in an elastic collision.

27. Xishem

In the real world, momentum is never conserved in collisions. When two pool balls hit eachother for instance, they release some sound upon impact -- this is lost energy. They are also always under the effect of friction from the table.

28. pratu043

Thanks.