Two particles approach each other with equal and opposite speed v. The mass of one particle is m, and the mass of the other particle is nm, where n is just a unitless number. Snapshots of the system before, during, and after the elastic collision are shown above. After the collision the first particle moves in the exact opposite direction with speed 2.95v, and the speed of the second particle is unknown. What is the value of n?

Question

caozeyuan · Answer

@perl

caozeyuan · Answer

@ganeshie8

4n1m0s1ty · Answer

So you need to use conservation of momentum to solve this, the equation is fairly straightforward. Is there a certain part you are having trouble with?

caozeyuan · Answer

Yes I got equations written down but don't know how to solve

caozeyuan · Answer

For conserv of p I have$$v-nv=2.95v+nv _{f}$$
and conserv of E gives $$(n+1)v ^{2}=(2.95v)^{2}+nv _{f}^{2}$$

caozeyuan · Answer

v is the v given in the question and v sub f is the undetermined velocity

caozeyuan · Answer

I got two eqa and two variable so supposedly I can solve to find n but not sure what to do

4n1m0s1ty · Answer

Just give me a few mins, trying to sort out an explaination.

caozeyuan · Answer

first of all: are the eqations correct.  I think I made no mistake but not 100% sure

4n1m0s1ty · Answer

Ok, so I have the solution right now. Sorry for the wait. I'll be posting it now.

4n1m0s1ty · Answer

So the first thing is that I think your first equation needs a negative sign on the third term.

$$v(1-n) = -2.95v + v_{f}$$

this is because the first object heads in the opposite direction, so i just reverse the sign. But everything else is setup correctly.

4n1m0s1ty · Answer

So now is just a lot of algebraic manipulation, I transform the first equation into this:

$$v_{f} = \frac{ 3.95v }{ n } -v$$

basically just get vf in terms of everthing else and simplify.

Then before I just plug this into the second equation, I do some more algebra to make the math somewhat easier:

$$(-7.7025 + n)v^{2} = nv_{f}^2$$

4n1m0s1ty · Answer

So, now I plug in the first eq. to the 2nd eq. and get this mess:

$$(-7.7025 + n)v^{2} = \frac {15.6025v^{2}}{n} - 7.9v^{2} + v^2n$$

4n1m0s1ty · Answer

So now you solve for n, and if I did my algebra right, all of the v's will cancel and you get this result:

n = 79

I'm a bit tired right now, its midnight where I am, so forgive me I messed up somewhere, but I'm pretty sure this is right.

4n1m0s1ty · Answer

any questions?

caozeyuan · Answer

thx

4n1m0s1ty · Answer

np