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Two blocks of masses m1 = 2.00 kg and m2 = 4.55 kg are each released from rest at a height of y = 4.10 m on a frictionless track, as shown in Figure P6.56, and undergo an elastic head-on collision. (a) Determine the velocity of each block just before the collision. Let the positive direction point to the right. v1im/s v2im/s (b) Determine the velocity of each block immediately after the collision. v1fm/s v2fm/s (c) Determine the maximum heights to which m1 and m2 rise after collision. y1fm y2fm http://img354.imageshack.us/my.php?image=p656altfk4.gif |
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a) Using energy v=sqrt(2*g*h) v1i=v2i=sqrt(2*9.81*4.10) 8.97 m/s b) Since the collision is elastic momentum and energy are conserved 2*8.97-4.55*8.97=2*v1f+4.55*v2f .5*2*8.97^2+.5*4.55*8.97^2= .5*2*v1f^2+.5*4.55*v2f^2 do a bunch of messy algebra 2*8.97-4.55*8.97=2*v1f+4.55*v2f v1f=-2.275*v2f-11.44 v1f^2=5.1756*v2f^2+52.04*v2f+130.8 .5*2*8.97^2+.5*4.55*8.97^2= .5*2*v1f^2+.5*4.55*v2f^2 263.51=v1f^2+2.275*v2f^2 substitute 0=7.45*v2f^2+52.04*v2f-132.71 v2f=1.9857 m/s v1f=-15.95 m/s c) Using energy h=.5*v^2/g Block 1 h=.5*15.95^2/9.81 h=13 m Block 2 h=.5*1.9857^2/9.81 h=0.20 m _______________- |
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