# How do you solve a spring problem involving a collision?

I was just learning about collision in class and I did some research online about it. I found a question which involved a collision and a spring. I know how to do spring problems and how to do collision problems but I'm not sure how to solve a problem involving both. If someone could explain a method to do these kind of problems, that would be greatly appreciated.

The question I found online is this:

A $10.0\ \mathrm{kg}$ block hangs (in equilibrium) from a spring of force constant $450.0\ \mathrm{N/m}$. A bullet of mass $45.0\ \mathrm{g}$ is fired upwards into the block at a speed of $150\ \mathrm{m/s}$. The bullet embeds in the wooden block. What is the maximum height the block rises to, relative to its initial position?

If some could provide a general strategy to solve problems similar to the one above (and use the given problem as an example), that would be great.

My work so far: I just tried based on what I know and found online. I treated the question as two different problems (not sure if this is the way to go or not). First I knew the collision was completely inelastic and I used conservation of momentum to find the momentum of the block and bullet assuming there was no sprint. I then found the speed of the block (with the bullet) and found kinetic energy. Since energy is conserved, I was able to find the height to be 27 cm above the starting position. Is this the correct way to do this (am I correct)?

I think I have done the conservation of momentum part correctly but I am not to sure about the conservation of energy part of it.

• Some people will probably think this runs afoul of our homework policy but I don't believe so, because it asks for a general method for doing these types of problems. Faiz, we won't show you a complete solution to the problem, but it's certainly fine to ask about the general approach. However, it would be a better question if you added some info about what you've done yourself to figure out how to solve these types of problems, and that will help us give you more focused advice. – David Z Apr 12 '18 at 2:10
• Hi David, I don't have any work to show because I have no way of even starting the problem. I was hoping that by posting this question, someone would guide me through the method for solving these kinds of problems. The question is not a homework problem but simply an example someone can use to answer the problem (if it helps them explain more clearly). Thanks :) – Faiz Momin Apr 12 '18 at 2:14
• I understand that you don't know how to solve it, but surely you could have checked some combination of textbooks, educational websites, videos, friends, teachers, fellow students, etc. Give us some idea of what you looked at. We have a list which shows some things you could try. People generally prefer to answer questions where the asker shows that they're willing to invest time and effort, just as the answerers are doing, and your question doesn't do that - that's why it's probably not going to be well received. – David Z Apr 12 '18 at 2:29
• I just tried based on what I know and found online. I treated the question as two different problems (not sure if this is the way to go or not). First I knew the collision was completely inelastic and I used conservation of momentum to find the momentum of the block and bullet assuming there was no sprint. I then found the speed of the block (with the bullet) and found kinetic energy. Since energy is conserved, I was able to find the height to be 27 cm above the starting position. Is this the correct way to do this (am I correct)? – Faiz Momin Apr 12 '18 at 2:34
• You method of using the conservation of momentum for the collision (no vertical external forces acting and applying a significant impulse) and then the conservation of mechanical energy (no dissipative forces, eg air resistance acting) is correct but remember that the block and bullet gain gravitational potential energy as well as the spring gaining elastic potential energy. – Farcher Apr 12 '18 at 8:23