Movement Simulation Problem

[nuclearist]

Hi. I am a physics teacher and i am new in Algodoo. So, could you help me to simule below question, please. Thanks a lot.

Suppose I have two identical masses, m1 and m2, that are both sliding along a frictionless horizontal surface with the same speed and direction. When they reach point A, m1 continues as before, but m2 drops into a depression in the surface. I'm not specifying anything about the shape of this depression except that it is smooth and continuous, and it does not drop so suddenly that m2 loses contact with it - in other words, gravity is sufficient to keep m2 on the surface (no cliffs or walls). Which mass will arrive at point B first?

[FRA32]

There are 2 cases:

A: m2 slides down, and does not keep enough velocity to come back up. This is usually the case if it drops from the surface when entering the hole, which is not the case here, or if it collides with uneven terrain, causing it to make tiny jumps up and down, loosing velocity in the process.

B: m2 reaches B first, since it accellerates after A, causing it's velocity to increase, and the time to pass the area between AB to decrease. Once it decellerates again, it returns to it's original velocity, but with the distance boost of the accellerated part, and reaches B first.

If you want to test this process in Algodoo, create a small box, and a larger box that acts as the ground. Reduce both their friction to 0, and optionally the restitution(helps keeping velocity). Then apply movement to the box while the scene is paused by using the Velocity menu and increasing X to something around 2 to 5. Then create multiple copys of both the floor and the small box, and change their collision sets to a new letter each. Then you can use the erasing tool, the cutting tool, or the CSG difference tool to create a hole in the copys, and after everything is set, move everything so that each part overlays the other. Remember to deactivate air friction so that the boxes don't slow down. If you run the simulation then, the boxes wont collide with each other since they don't share collision sets, and each takes the path it's sharing collision with. You will notice how some boxes stay in the depression, while some get out and usually pass past the box that takes the straight path.


Hope this helps

[nuclearist]

Thank you FRA32 for your reply. I attached phz file that i created. I think, it is enogh for me and for my students. m2 mass slow down a bit. But thats all i could do.

[FRA32]

Of course there can be minimal losses of velocity due to rounding errors or minimal inpulses against the ground. But it should be clear that m2 is faster thanks to the accelleration, and that it returns to about the same velocity as at the beginning.