Blocks A (mass 6.50kg ) and B (mass 14.50kg ) move on a frictionless, horizontal
ID: 2199591 • Letter: B
Question
Blocks A (mass 6.50kg ) and B (mass 14.50kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 3.00 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. 1) Find the velocity of A. 2) Find the velocity of B.* ***NOTE: I tried the answers -1.14, and 1.86, but mastering physics said they were wrong. Please help.Explanation / Answer
the conservation of momentum , m1u1+0 =(m1+m2)V V = 4.5/19.5 = 0.23 m/s the velocity of A&B is 0.23 m/s. the maximum energy store is equals to the change in K.E of the system. ?K.E =1/2*4.5*1.0- 1/2*19.5*(0.23)^2 = 2.25-0.519 = 1.730 J the maximum energy stored spring bumpers is 1.730 J. the maximum energy = 1.730 J According to conservation of momentum and elastic collision, m1u1+0 = m1v1 + m2v2 ---------------- (1) u1 = v2-v1 ------------------ (2) From equation (1)&(2) m1u1 = m1(v2-u1) + m2v2 2m1u1 = v2(m1+m2) 2*4.50*1.0 = v2(19.5) v2 = 0.461 m/s and v1 = -0.538 m/s