Blocks A (mass 6.50kg ) and B (mass 14.50kg ) move on a frictionless, horizontal
ID: 2199539 • 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. 3) Find the velocity of each block after they have moved apart. *Note: part 3's velocities are -1.14, and 1.86. I don't know how to determine part 1 or 2. I tried putting in the initial velocities, 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