What Are the Final Velocities After an Elastic Collision Between Two Books?

[rootX]

Homework Statement

A physics book is thrown @ 12 km/h [N 28 E] mass = 1.54 kg
and a chemistry book @ 9 km/h [N 65 W]; mass = 1.82 kg

if they collided in an elastic collision find final velocities of each book.

Homework Equations

those two momentum-energy conservation formulas.

The Attempt at a Solution

so, I assumed that frame of ref. is moving @ 9 km/h [N 65 W]
and then found relative velocities, and using those two formulas find the velocities of both books, and again converted the final relative velocities to original vs.

and got 9.75 km/h [N59 W] for the physics book, and 11.07 km/h [N 32 E] for the chemistry book.
I am not sure about my answers because I had to do many calculations, and if you can check them for me?
<is there an easier way to solve such problems?
I was wondering about center of mass thing, but I did not try using that way because I really dunn know if that would be an easier way and also I dunn even know how to find the velocity of the center of the mass of this system>

 

[denverdoc]

I'm not surprised the chemistry book was heavier, due to all the excessive handwaving that goes on with such a lesser science.

I must admit that I am unfamiliar with your method of solution, the approach i was taught is a bit different. First you need to figure the angle of impact, and by resolving the momenta into components that are axial and perpendicular, it becomes a 1-D problem, with the usual eqns derived by conserving both momenta and energy. The tangential components are unaffected but then need to be added back to the 1D results to get correct vectors.

Let me hunt around a bit, iirc there is an applet that will let us check the results on line as I certainly have better things to do.

 

[Mindscrape]

Hah, I thought that the question would be about a complex momentum, as in root(-1). A little disappointed.

So you used relativity to "simplify" the problem? Your method is fine, though I have not checked the calculations either.

The way you could check is to use a ground reference frame the whole way through, and see how the answers compare.

 

[denverdoc]

Mindscrape, I'm intrigued. I have used similar principles such as even imposing an accelerating inertial frame of reference (which is allowed by both Newton and Einstein) to solve some simple problems. Gimme the gist or a good link, and I'll be really appreciative.

OP: here's the applet, I wouldn't worry about converting to m/s the results should be the same. You can move the balls around to get the right angle, sort of a fun applet, but stop it after the desired collision or it becomes a perpetual pool game with refeshed results.
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=4

 

[Mindscrape]

The idea is that you use relativity to make one of the objects "at rest" before the collision. Then you analyze the collision according to your "at rest" frame, and figure out the vectors. After you have done that you simply convert it back to the original inertial "ground" reference frame. Though it will only work for perfectly elastic collisions because inelastic collisions will lose energy and be non-inertial. However, since the collision is elastic, energy is conserved, and everything stays inertial, the analysis in one frame will be equally valid as in some other, and no information will be lost when converting between the two.

Tried finding in one of my physics books to take a picture of, but can't, sorry.

 

[denverdoc]

thanks that was very helpful.

 

[rootX]

thanks a lot! =P