Question

6. Consider a horizontal spring with spring constant k. A block with mass m is pushed far to the left against the spring until the spring is compressed a distance r relative to its relaxed length. A second block, which is stationary and also has a mass m, is located to the right of the spring im rrm a) We release the first block from rest. Due to the force from the spring, it slides to the right and eventually collides with the second block. You may assume the second block is far enough to the right that the first block is not in contact with the spring when the blocks collide. Let's also assume the blocks stick together after the collision. Find an expression for the speed of the blocks in terms ofm, k, and r after the collision b) Let's assume the blocks remain stuck together at all times, so we can think of them as a single block with a combined mass 2m. The block of mass 2m collides elastically with the wall and then slides back towards the spring. When the block comes to a rest, the spring will be compressed some distance ri. What is the ratio 1/r? c) Now suppose that while 2m is in contact with the spring, we place another block with mass m to the right of 2m Eventually, the spring will push 2m to the right and it will collide with m. The block of mass m is initially stationary and it is far enough to the right that 2m is no longer in contact with the spring when 2m and m collide. After the collision, the blocks 2m and m stick together at all times so we can think of this as one block with a combined mass 3m. The block of mass 3m collides elastically with the wall, and then slides back towards the spring. When the spring brings 3m to rest, it will be compressed some distance r2. What is the ratio r2/x? Now suppose we repeat this process until there have been a total of n collisions between blocks (the collision in part a) is collision 1, the collision between 2m and m is collision 2, and so on). When the spring brings this conglomeration of blocks to rest it will be compressed some distance rn. What is the ratio rn/r?

Answer 1

4 づ wiit づ 3 즉,