Blue Elastic
Sep/080
Physics perfectly elastic collision problem with pucks?
I can't seem to figure this one out after using the equations my teacher gave me. I don't know what I'm doing wrong. Please help!
A blue puck with a mass of 3.50×10−2 kg, sliding with a speed of 0.200 m/s on a frictionless, horizontal air table, makes a perfectly elastic, head-on collision with a red puck with mass m(red) , initially at rest. After the collision, the velocity of the blue puck is 4.00×10−2 m/s in the same direction as its initial velocity.
a. Find the velocity v(red) of the red puck after the collision.
b. Find the mass m(red) of the red puck.
In thoughtdream's 3rd paragraph he assumes the masses are equal. That's the only way he could find Vr so easily.
I spent a while on this last night and here are the results:
The velocity of the center of mass of Mb & Mr combined is the same before and after the collision.
Vc = (MbVb + MrVr)/(Mb + Mr) = .007/(.035+Mr) ...........(1
The change in momentum of blue = the negative of the change in red:
∆Pb = -∆Pr → Pr = -.035(.04-.20) = .0056 = MrVr............(2
The velocity at which Mr recedes from the center of mass is
Ur = Vb/(1+Mr/Mb). Therefore, using (1,
Vr = Vc + Ur = .007/(.035+Mr) + .20/(1+Mr/.035) .............(3
By putting (3 into (2 gives an eq in Mr only which can be solved. I got Mr = .02333 kg.
Then use (2 again to find that Vr = .24 m/s
To check this, the total initial momentum is .035*.20 = .007
Final momentum is .035*.04 + .02333*.24 = .007 kg.m/s
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