- #1
deborahlane
- 3
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Homework Statement
I have two particles moving on a smooth horizontal table. The first, A, has mass m and the second, B, has mass 3m. A has velocity 2i + 3j and B has velocity 6i - 5j. They collide at the origin at t=0 and coalesce.
I have to 1) determine the velocity of the coalesced particle after the collision; 2) determine the amount of energy lost in the collision; 3) find expressions for rA(t) and rB(t) at time t<0; 4) find the position vector of the centre of mass of the system before the collision; 5) determine the velocity of the centre of mass; 6) find the position vector of the coalesced particles at time t>0 after the collision; and 7) comment on the answers to parts 3)-6)
Homework Equations
I've used the following: 1) Total linear momentum of system P=mv and found P of A is 2mi + 3mj and P of B is 18mi - 15mj, so using the Principle of conservation of momentum, I found v of coalesced particle to be 5i - 3j
2) kinetic energy=1/2mmodv2 and KE before impact is 98m and after is 68m, so loss is 30 joules.
4) rG=[tex]\Sigma[/tex]miri all divided by total mass...when I finally find the position vectors!
5) Velocity of the centre of mass=total linear momentum of the system...I think.
6) With position vectors for A and B, I'm not sure what to do here: add them, since the particles coalesce?
The Attempt at a Solution
3) My problem is from 3) onwards. I'm pretty sure I can figure out the rest of it once I have 3). I can't work out how to get from the velocity vectors to position vectors. I thought of integrating and using t=0 r=0 to find a particular solution, but that seems to just leave me with rA(t)=2ti + 3tj and rB(t)=6ti - 5tj, which just doesn't seem to make sense.
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