Blocks A (mass 4.50 kg ) and B (mass 13.00 kg ) move on a frictionless, horizont
ID: 2213443 • Letter: B
Question
Blocks A (mass 4.50 kg ) and B (mass 13.00 kg ) move on a frictionless, horizontal surface. Initially block B is at rest and block A is moving toward it at 7.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of A ,,,,,,,,,,,,,,,,,,, Find the maximum energy stored in the spring bumpers and the velocity of each block at that time. Find the maximum energy ? Find the velocity of A ? Find the velocity of B ? Find the velocity of each block after they have moved apart. Find the velocity of A ? Find the velocity of B ?Explanation / Answer
Let's answer the final-velocity question first: Total momentum = (6.00 kg)(8.00 m/s) = 48 kg-m/s After collision (elastic): KE = 0.5 mv^2 = 3.00(64) = 192 J 192 J = 3v1^2 + 7.5v2^2 m1v1 + m2v2 = 48 kg-m/s ------------------ v1 = 48/m1 - m2v2/m1 v1 = 8 - 2.5v2 192 J = 3v1^2 + 7.5v2^2 192 J = 3(64 - 40v2 +6.25v2^2)+ 7.5v2^2 Write this quadratic equation in standard form, and solve for v2. -------------- Note on energy storage in spring: The problem does not provide sufficient information. If we simply assume that the KE is all stored in the spring, during the collision, then the stored energy = 192 J. --------------------