This problem is a standard 1-D problem. You have 2 equal carts approaching each other and collide on linear air track.
BUT the person setting up the track did NOT do a good job at making the track Level(or NOT perfectly horizontal).
THE QUESTION is : HOW "UNLEVEL" is the track?
The collision took t= 0.750 seconds.
And the data collected is below:
DATA
m1=m2= 1kg
Initial velocities:
v1i= +0.450m/s
v2i= -0.505m/s
Final velocities:
v1f= -0.510m/s
v2f= +0.420m/s
From the data we can easily calculate the momentum before and after the collision and
see that the momentum of this system is NOT Conserved.
To me this makes sense because the track is unlevel, we have made the track to be like
an inclined plane which means that gravity now has influence on this system!
SO we have now gone into 2-D space, and we have acceleration happening due to gravity.
I was able to figure out this much.
BUT how do I calculate, based on the given information, say the angle that the track makes with respect to the horizontal.(This is what I guess the question is asking).
BUT, I also don't understand how they can measure the velocities(in the data given) if
we have acceleration, which means that the velocity is changing(velocity is no longer constant).
SO I see some contradictions here in this question.
I found this question in an old book, and there are no answers to the questions.
BUT this one got me interested.
Hope somebody has seen this kind of question before.
Your help is greatly appreciated.
Palu
Best Answer
Variation of momentum means force: $F = \dot p$. In a very non-rigorous way, we have: $$ F = \frac{dp}{dt} \quad\Longrightarrow\quad Fdt = dp \quad\Longrightarrow\quad F = \frac{\Delta p}{\Delta t} $$
The force in this case, it is likely assumed to be the gravitational force: $F = mg\sin\theta$, where $\theta$ is the angle of the ladder and the horizontal axis, and $\Delta t$ is the time taken by the collision. Hence: $$ \sin\theta = \frac{\Delta p}{\Delta t}\frac{1}{mg} $$