- #1
aeromat
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Homework Statement
Q: Two air track gliders of masses 300g, and 200g move towards each other in opposite directions with speeds of 50cm/s and 100cm/s respectively. Take the direction of the more massive glider as positive.
If the collision is elastic, find the velocity of each glider AFTER collision
[Given answer for the question: [-70cm/s, 80cm/s], but I'm not sure if that is respective to the gliders themselves]
Let A be the 300g plane
Let B be the 200g plane
Homework Equations
[1]---> MAVA + MBVB = MAV'A + MBV'B
[2]---> 1/2MVA^2 + 1/2MVB^2 = 1/2MV'A^2 + 1/2MV'B^2
1/2's are canceled out, so we get:
[2] MVA^2 + MVB^2 = MV'A^2 + MV'B^2
The Attempt at a Solution
Isolated V'B in the momentum conservation equation to get the following:
V'B = [tex]\frac{MAVA + MBVB - MAV'A}{MB}[/tex]
V'B = [tex]\frac{(300)(50) + (200)(-100) - 300(V'A)}{200}[/tex]
Subbed into the kinetic energy conservation equation:
[tex]MAVA^2 + MBVB^2 = MAV'A^2 + MB(\frac{MAVA + MBVB - MAV'A}{MB})^2[/tex]
Let V'A rep [tex]x[/tex]
[tex](300)(50)^2 + (200)(-100)^2 = (300)(x)^2 + 200(\frac{(300)(50) + (200)(-100) - 300(x)}{200})^2[/tex]
At this step, I am doubting whether or not I should countinue doing it this way. Is there any other algebraic method to get the two velocities after the collision, being it an elastic collision? I carry out this entire question taking up about half a page and then find myself scratching my head over a wrong answer...