Hello again, pj4444
This problem can be solved once you know the following. Firstly, that
in all collisions, momentum is conserved. Thus, we have that:
ma*va0 + mb*vb0 = ma*vaf + mb*vbf
where ma is the mass of object a, va0 is the velocity of object a
before collision, vaf is the velocity of object a after the collision,
and mb, vbo and vbf are similarly defined for object b. In all terms,
m*v is momentum.
Also, we know that since this is a prefect elastic collision, kinetic
energy is conserved:
(1/2)*ma*va0^2 + (1/2)*mb*vb0^2 =
= (1/2)*ma*vaf^2 + (1/2)*mb*vbf^2
Now, from the problem, we know that ma=0.300, mb=0.600, va0=2.50 ms-1,
and vb0=1.00 ms-1. Both velocities are positive because the problem
states that they are moving in the same direction. If they were moving
in opposite directions, one of the m should be negative and the other
positive. From now, I will also assume that both balls are moving
"forward".
So, with both equations, the problem is easy to solve. It's just a
system of 2 equations and 2 unkowns (the unknowns being vbf and vaf).
In the following page, you will find the solution to this system.
Physics - Collision in 1 dimension
http://www.martinb.com/physics/dynamics/collision/oned/
I'll write here the final result:
vaf = vai*(ma-mb)/(ma+mb) + vbi*2*mb/(ma+mb)
vbf = vbi*(mb-ma)/(ma+mb) + vai*2*ma/(ma+mb)
Plugging the numbers you provided in these equations gives
vaf = 2.5*(0.3-0.6)/(0.3+0.6) + 1*2*0.6/(0.3+0.6)
= 0.5 ms-1
vbf = 2 ms-1
That is, both balls are still moving "forward" (there is no change in
direction) and their new velocities are 0.5 ms-1 for the 0.300 kg ball
and 2 ms-1 for the other one.
For addition resuources on this subject, you may want to visit the
following pages:
Linear Momentum - Collisions
http://www.sparknotes.com/physics/linearmomentum/collisions/section1.html
Physics Tutoring - Collisions
http://www.slcc.edu/schools/hum_sci/physics/tutor/2210/collisions/
Hope this helps!
Best regards,
elmarto |
