Mechanics - Momentum

I've been given 2 particles, one of unknown mass (m), the other of a mass of 5kg, with the unknown one having a velocity of (3i+2j)ms-1 and the other with a velocity of (-2i-1j)ms-1. They then coalesce and move with a velocity of (1.75i + vj)ms-1.

I have to find m and then find v. I've tried writing them out using the conservation of momentum equation and i'm not sure if it's just me not cancelling out things I should be, or making a daft calculating error, but I can't seem to find m. It seems to throw me off since there are 2 unknowns in there. Am I going about this the right way or is there something else I should know/do?

Many thanks

Reply 1

Phugoid

Simonc89

I've been given 2 particles, one of unknown mass (m), the other of a mass of 5kg, with the unknown one having a velocity of (3i+2j)ms-1 and the other with a velocity of (-2i-1j)ms-1. They then coalesce and move with a velocity of (1.75i + vj)ms-1.

I have to find m and then find v. I've tried writing them out using the conservation of momentum equation and i'm not sure if it's just me not cancelling out things I should be, or making a daft calculating error, but I can't seem to find m. It seems to throw me off since there are 2 unknowns in there. Am I going about this the right way or is there something else I should know/do?

Many thanks

Remember that momentum is conserved in ALL directions. In other words, if you split this problem up into two parts:

1) In the first part, consider ONLY the quantities in the i direction, then you will have NO unknown velocities, and can calculate the mass.

2) In the second part, consider ONLY the quantities in the j direction, then you will have only one unknown, the velocity, since you calculated the mass in part 1.