Hello.

I am a bit confused on a question concerning linear elastic and inelastic collisions. I see that two characteristics of a completely inelastic collision are first that the sum of the initial and final momentums are equal, or:

and second, that after the collision both objects stick together. If we assume that the second object involved in the collision is initially stationary, and we wanted to solve for a final velocity of this second object, we can then write the above formula as:

About elastic collisions we know that kinetic energy before the collision is equal to kinetic energy after the collision. We can write this with the following equation:

Again, assuming the initial velocity of our second object is zero, and solving this for a final velocity of the second object we get:

What I want to figure out is which type of collision will have a higher likelyhood of closing the door. The parameters given are:

= .4 kg

= 30 kg

= 1 m/s

= 0

The solution I come up with is that while the inelastic collision gives a precise value of final velocity, the elastic collision gives a range of values that includes the value for the final inelastic velocity. Using what information I have worked out, I conclude that neither type of collision is more or less likely to close the door since the elastic collision could give both a value of velocity greater and lesser than the velocity given by the inelastic collision.

Would someone be kind enough to go over the work I have shown above and tell me what you think about it? My intuition tells me that if you know that a collision is an elastic or inelastic collision and you knew all the initial variables, you should be able to predict the outcome. This should include the final velocities of both objects.