# Locating point of impact "during" elastic collision (1D)!

We have two objects moving opposite to each other on the x-axis. They started to collide on the location $$x = 0$$ on x-axis.

• We know that if object one $$m_1 = 10 kg$$, and $$v_1 = 10 m/s$$, and object two $$m_2 = 10 kg, v_2 = -10 m/s$$, then during the entire collision process (time of impact) the point of impact will remain on $$x = 0$$.

• a. If $$m_1 = 10 kg, m_2 = 10 kg, v_1 = 10 m/s, v_2 = -20 m/s$$.

• b. If $$m_1 = 20 kg, m_2 = 10 kg, v_1 = 10 m/s. v_2 = -10 m/s$$.

• c. If $$m_1 = 20 kg, m_2 = 10 kg, v_1 = 20 m/s, v_2 = -10 m/s$$.

• d. If $$m_1 = 20 kg, m_2 = 10 kg, v_1 = 20 m/s, v_2 = -5 m/s$$.

• e. If $$m_1 = 20 kg, m_2 = 10 kg, v_1 = 5 m/s, v_2 = -10 m/s$$.

During the period of collision (during time of impact), does the point of impact stay on $$x = 0$$ till the collision fully finished, or does it move while the collision is happening. If it moves then where exactly. Let's suppose that our objects are both spheres with $$1\ cm$$ diameter.

This scenario is meant to be comparing both when having two ideal elastic spheres (whatever that actually could mean in term of elastic properties during a collision), and two actual metallic spheres. Finally, I don't actually seek exact numeric values as the answer, I just want descriptive explanations.

The motive for this question is an attempt to have a theoretical model of transforming kinetic energy into elastic potential energy and work, and then back to kinetic energy during the collision process. The relation between elastic potential energy and work, whether they coexist or cause each other sequentially. I have many struggles in supposing such model, and this question is regarding one aspect of those struggles, specifically, the point of impact location along the x-axis can be useful in determining the displacement during the work being performed by each object on the other.