Question

Problem 6. v- (for both) A small block with mass m is sitting on a large block of mass M that is sloped so that the small block can slide down the larger block. There is no friction between the two blocks, no friction between the large block and the table, and no drag force. The center of mass of the small block is located a height H above where it would be if it were sitting on the table and both blocks are started at rest (so that the total momentum of this system is zero, note well!) a) Are there any net external forces acting in this problem? What quantities do you expect to be conserved? b) Using suitable conservation laws, find the velocities of the two blocks after the small block has slid down the larger one and they have separated. c) To check your answer, consider the limiting case of Mo (where one rather ex pects the larger block to pretty much not move). Does your answer to part b) give you the usual result for a block of mass m sliding down from a height H on a fixed incline? d) This problem doesn't look like a collision problem, but it easily could be half of one Look carefully at your answer, and see if you can determine what initial velocity one should give the two blocks so that they would move together and precisely come to rest with the smaller block a height H above the ground. If you put the two halves together, you have solved a fully elastic collision in one dimension in the case where the center of mass velocity is zero!

Answer 1

"Given that The solution for the following Question is as follows: - The Diagramatic representation \r\n from the law of conservation of energy (K.Energy + P. Energy)_initial - (Kinetic Energy + potential energy)_Final [where V = 0] 0 + mgh = 1/2 m V_1^2 + 1/2 m V_2^2 2mgh = mV_1^2 + mv_2^2 equation (a) The system is ""0"" (from law of conservation of moment) mv_2 - mv_1 = 0 equation (b) mv_1 = mv_2 where V_1 = m_1 V_2/m equation (c) \r\n a) given that net external forces Acting on the system F_external = Change in the momentum = P_final - P_initial = mv_2 - mv_1 = 0 where [mv_2 - mv_1 = 0] F_external = 0 C) given limiting case of M rightarrow alpha where v_2 = 0 v_1 = alpha The entire system is ""0"" due to Momentum \r\n d) Consider the two Block, moves one on other, if there is no friction Between these two due to law of Conservation "