The blocks are equipped with ideal spring bumpers. The collision is head-on, so

Question

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 be the direction of the initial motion of .
1.Find the maximum energy stored in the spring bumpers and the velocity of each block at that time.
Find the maximum energy.
2.Find the velocity of A
3.Find the velocity of B
4.Find the velocity of each block after they have moved apart.
Find the velocity of A.
5.Find the velocity of B

Please show me how to work this problem..detail your answers

Explanation / Answer

By using conservation of energy. change in gravitational potential energy = change in kinetic energy or mgh = 1/2mv^2. In other words, the potential energy is converted into kinetic energy when an object falls. Example A 0.1kg ball falls from 10m. Take gravity to be 10m/s^2. Find the maximum velocity of the ball. mgh = 1/2mv^2 0.1 * 10 * 10 = 1/2 * 0.1 * v^2 10 = 0.05v^2 200 = v^2 v = square root(200) v = ~ 14m/s. Here goes, to solve for maximum energy stored initially, you find the change in Kinetic energy using the following: Change in Kinetic Energy= Kinetic Energy Final - Kinetic Energy Initial *(realize that this answer may be negative sometimes but that your answer in reality is positive because you are simply looking for the change in velocity not what direction the change occured so an answer of -38 means a change of 38 since we are only want to know what the Change in Kinetic Energy was)* So before we answer the "Maximum Energy" part of the problem, we first need to know the velocity of the blocks at the time of the collision. To find the velocity of each block at the time of the collision, we use conservation of momentum m1v1=(m1+m2)v2 m1 is the mass of block A and m2 is the mass of block B. The trick here is to realize that when the two blocks are closest to each other (when they are about to go off in different directions) they have the same velocity. It makes sense if you think about about two blocks with ideal springs hitting together on a frictionless plane.Therefore, they're both going to have the same v2. Cool Beans. So using this, find v2 and that will be your answer for both velocities of part A since they both share the same velocity at this point. Now, plug in this V2 for your final Kinetic Energy formula: Final energy = (0.5)(mA+mB)(v2^2) Initial energy = well, the only thing that has kinetic energy in the beginning is the block that is moving so the equation here is (0.5)(mA)(v1A^2) Final-Initial= the change in energy which is the maximum energy that could have been stored in those springs. Part B: To find the velocity of each block after they've moved apart will be a bit more difficult to remember but if you can remember these two equations for a situation where 1 block is already at rest, you should be golden. When 1 block is at rest your book should tell you that you can find VA2 and VB2 (final velocities of blocks A and B respectively) using the following equations: VA2= [(mA-mB)/(mA+mB)]*VA1 VB2= [(2*mA)/(mA+mB)]*VA1 One of your answers will be a negative velocity and the other will be a positive velocity, which makes sense because after the crash both blocks should be heading in different directions. Again, memorize the two equations for VA2 and VB2 when one is at rest. It makes your life much easier and you won't have to use the conservation of momentum and conservation of kinetic energy to solve since those will only get you lost when dealing with a block that is initially at rest.

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