2 bodies spining and cut in the middle

[york]

M1 and M2 are rigid bodies that connected. they spin freely around the Z-axis. At a certain time (we will set t=0) when the bodies are in the state described below, the bodies disconnect from each other when each of the bodies is given a speed addition in the direction of the X(V1 and V2 axis respectively). The separation speed is defined as the Vsep=V1-V2 speed difference. What is the minimum separation speed required in order not to cause no harm between the bodies?

 

[york]

M1 and M2 are rigid bodies that connected. they spin freely around the Z-axis. At a certain time (we will set t=0) when the bodies are in the state described below, the bodies disconnect from each other when each of the bodies is given a speed addition in the direction of the X(V1 and V2 axis respectively). The separation speed is defined as the Vsep=V1-V2 speed difference. What is the minimum separation speed required in order not to cause no harm between the bodies?

 

[berkeman]

M1 and M2 are rigid bodies that connected. they spin freely around the Z-axis. At a certain time (we will set t=0) when the bodies are in the state described below, the bodies disconnect from each other when each of the bodies is given a speed addition in the direction of the X(V1 and V2 axis respectively). The separation speed is defined as the Vsep=V1-V2 speed difference. What is the minimum separation speed required in order not to cause no harm between the bodies?

Welcome to PF.

Sorry, but I'm not able to understand what you mean by "in order not to cause harm between the bodies"? What kind of harm? When the attachment is severed, they fly off in different directions, no? Can you please clarify more? Thanks.

 

[york]

Welcome to PF.

Sorry, but I'm not able to understand what you mean by "in order not to cause harm between the bodies"? What kind of harm? When the attachment is severed, they fly off in different directions, no? Can you please clarify more? Thanks.

i mean that I want the minimum separation speed required which the bodies won't collide, thank you. the bodies severed exactly in the position in the picture

 

[berkeman]

What are (S1,Y1) and (X2,Y2)? What is that dark line enclosing the area where M1 is? Can you draw the vectors V1 and V2 at the instant that the masses are released?

 

[york]

the dark line enclosing the area in body 1. X1,Y1 you mean the coordinate of c.m?

 

[berkeman]

the dark line enclosing the area in body 1. X1,Y1 you mean the coordinate of c.m?

Sorry, I'm still not understanding the setup at all. I don't understand the function of the dark line around M1, and I don't understand what the coordinates (X1,Y1) and (X2,Y2) represent. And I don't understand the significance of the shaded areas.

My impression so far is that there is a string that hold M1 to the left side of the dark line (is that the origin), and another string that connects M1 and M2. The masses are circulating the origin in a counter-clockwise direction (uniform circular motion). At time t=0 both strings are cut, and M1 flies off with vector velocity V1 and M2 flies off with vector velocity V2.

Is that even close?

 

[york]

yes, I think you right so far

 

[berkeman]

So the 2 mass velocity vectors V1 and V2 are pointing straight up at the moment t=0. So M1 crashes into that dark line enclosure and M2 keeps on going straight up?

 

[york]

no, first when the bodies severed there c.m each has a velocity only in y axis, the velocity in x-axis is xternal insert.

 

[berkeman]

the bodies disconnect from each other when each of the bodies is given a speed addition in the direction of the X(V1 and V2 axis respectively). The separation speed is defined as the Vsep=V1-V2 speed difference. What is the minimum separation speed required in order not to cause no harm between the bodies?

So at the instant t=0, the two masses also are given x-velocities of V1 and V2, and you want to relate those velocities to the initial Y-direction velocities to ensure that the masses don't come together somewhere above and to the right of the origin?

Okay, now that we've gotten that sorted out (whew!), what do your equations look like so far?

 

[york]

So at the instant t=0, the two masses also are given x-velocities of V1 and V2, and you want to relate those velocities to the initial Y-direction velocities to ensure that the masses don't come together somewhere above and to the right of the origin?

Okay, now that we've gotten that sorted out (whew!), what do your equations look like so far?

this is where i stuck, i think i understand what happened but i don't know how to write it down

 

[berkeman]

Just write the equations for the x & y motion of each of the masses based on their initial velocity vectors and position vectors from the origin. Then you should be able to find an equation that gives you the minimum (or maximum?) value of V2-V1 so that the two masses do not come together anywhere...

 

[haruspex]

the dark line around M1, and I don't understand what the coordinates (X1,Y1) and (X2,Y2) represent. And I don't understand the significance of the shaded areas.

I believe the thick dark line is M1 and the shaded area is M2. The circles with crosses are the locations of their mass centres. X1, Y1 etc. show the shapes of the masses.

Since the X distances are shown as from the left end of M1 I presume the axis of rotation is the left end of the dashed-dotted line, not where the rotation symbol is shown. But it might not matter which.

To solve it, one will need to consider how the mass centres move after release and how the bodies continue to rotate.

 

[berkeman]

I believe the thick dark line is M1 and the shaded area is M2. The circles with crosses are the locations of their mass centres. X1, Y1 etc. show the shapes of the masses.

Oh my, I didn't see any of that. Thanks @haruspex !

 

[Lnewqban]

i mean that I want the minimum separation speed required which the bodies won't collide, thank you. the bodies severed exactly in the position in the picture

How could the bodies collide?
I believe that the separation trajectory will be radial respect to the center of rotation, which has not been clearly specified yet.

 

[haruspex]

How could the bodies collide?
I believe that the separation trajectory will be radial respect to the center of rotation, which has not been clearly specified yet.

Think what the trajectory and velocity of each is when no external force acts.