Question

2) Figure 2 illustrates a pair 1st and 2nd blocks having respective masses Mi and M2. The blocks are positioned on a horizontal frictionless plane.The 2nd block is initially at rest and the first block is traveling with an initial speed vı along the positive x-axis such that there is a collision with the 2n block. The 1st block includes an ideal spring having natural length L extending from its front end such that the spring is compressed when the distance, D, between the blocks is less than L. While the spring is compressed, the momentum of the 1st block decreases and the momentum of the 2nd block increases Eventually, the spring returns to its natural length and it is no longer in contact with the 2nd block. Assume there is no dissipative work being done on the system of blocks/spring during the collision. Figure 2 2 a) While the spring is compressing, the relative speed between the blocks is increasing, decreasing, zero). While the spring is expanding back to its natural length, the relative speed between the blocks is compressed, the relative speed between the blocks is energy of the system has a (choose one of these (increasing, decreasing, zero). At the moment the spring is maximally (increasing, decreasing, zero), and the kinetic value (zero, maximum, minimum) b) Determine an expression {Mi, M2) .for the ratio of the minimum kinetic energy of the system divided by the initial kinetic energy of the system; c) Determine expressions {vi, Mi, M2j for the speed of each block when the spring returns to its natural en

Answer 1

When block-1 collides with block 2 spring compresses and exerts a force on both block in the direction shown below Fx m, Spring force is in the direction opposite to motion of block 1 so speed of block I decrease and spring forces accelerate block 2 so its speed increases, this happens until both the blocks have same speed equal to speed of center of mass at this time spring has maximum compression (maximum PE) and kinetic energy is minimum comMM2 in the center of mass frame both block remains stationary when compression is maximum Vcor/ 3 rAx m2 So relative speed between the blocks at this time is zero

After this spring relaxes and attains natural length transferring its stored potential energy into kinetic energy of blocks while the spring is compressing, relative speed between the blocks is decreasing while the spring is extending back to its natural length relative speed between the blocks is increasing At the moment the spring is maximally compressed relative speed between the blocks is zera and the kinetic energy of the system has a minimum value 2 2 KEmin 2 KEmin KE, (M+M when spring returns to its natural length velocity of both the blocks is

Vi, V, from momentum conservation Vi- V from energy conservation

1 22-21 1 22 21 2 2 2 2