I need some help with the following question. A square with mass $M$ is at rest on a frictionless surface and a point-like particle with mass $\frac{M}{2}$ hits it's top corner with velocity $v_0$. What is the maximum speed of that particle?

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So for that part I tried to calculate the initial $\omega$ with respect to the bottom right corner, but couldn't carry the calculations. What is the answer to this question? Also, there is a follow-up question that states that a second mass $\frac{M}{4}$ falls on the square such that the CoM speed is constant, does this mean that it is necessarily not rolling? Thank you!

  • $\begingroup$ Does the particle bounce off, or embed itself to the block? $\endgroup$ Jan 17 at 22:52

So there is an equal and opposite impulse $J$ acting on the block due to the particle, and also two reaction impulses $A$ and $B$ acting from the ground to the corners of the block


Using conservation of linear momentum you can find $J$, which is then used to find $A$ and $B$ using the fact that $M$ should not tip over.

  • $\begingroup$ Would the mass roll about it's CoM or around the bottom corner? And could you please explain what are A and B? I just calculated the moment of inertia of the box+mass, but I defined it to be around the corner which could be incorrect $\endgroup$
    – Omer Paz
    Jan 18 at 8:24
  • $\begingroup$ Yes, the block will tend to rotate about the far corner. That is the pivot point. $\endgroup$ Jan 18 at 18:02

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