Two identical pucks B and C , each of mass m , are connected by a rod of length

Question

Two identical pucks B and C, each of mass m, are connected by a rod of length l and negligible mass, that is free to rotate about its center. Puck A, of mass m/2 comes in and hits B. After the collision, in which no energy is lost find: a) the rotational speed of the dumbbell and b)the velocity and of puck A

I have asked several people and have gotten several answers, which one is correct?

A first answered:

V_Afinal= -(V_Ainitial)/3

=(8/9)((V_Ainitial^2)/(l))

another answered:

After hitting there is no energy loss, it means that the Kinetic energy is conserved and momentom is also conserved

m/2 is the mass of puck a

m is the mass of pucks b and c

Since the kinetic energy is conserved we can write the conservation as,

1/2mv2=1/2Mv22+1/2Iw2

w=mvd/I (WHERE DID w=mvd/I COME FROM, is it mvd=Iw?? )

Substituting w we get

1/2mv2=1/2Mv22+1/2*I*(mvd/I)2 (why do we consider the angular momentum of the dumbbell and the angular momentum of puck B? in other words why isnt 1/2mv2=1/2*I*w?)

divide by m2v2

1/m=1/M+d2/I

m=1/(1/M+d2/I)

m=12mML2/(1/12)ML2+Md2)

m=ML2/(L2+12d2)

By conservation of momentom,

mv=Mv2

v2=v*(m/M)

So,v2=(v/M)*(ML2/(L2+12d2))

We know that mvd=Iw

w=mvd/I

So angular speed,w=vdML2/(L2+12d2)I

A third answered:

=(4/5)((V_Ainitial)/(l ))

V_Afinal= -(3/5)(V_Ainitial)

A fourth answered:

V_Afinal= V_Ainitial - 2l 2

= -4/(4l 2 - 1)

Who gave the correct answer, and why are the incorrect ones incorrect?

Explanation / Answer

Yes mvd = Iw (This is what is the conservation of angular momentum for this case)
The second question is a good question: You have misread the equation.
It says that initial kinetic energy with puck A = final kinetic energy with puck A + new kinetic energy with set of B and C

Because of this reason we cannot just write 1/2mv2 = 1/2Iw2

because there will be some energy that will stay with puck A
Note that puck B and C are as a set and the conservation of momentum is not valid in their case. Only angular momentum is conserved. As a rule of thumb remember for your problem solvings that when impacts happen of extended bodies (not point size bodies like electrons or sometimes spherical balls) then we consider only angular momentum conserved and not linear momentum conserved.

Coming to your last question: It is impossible to tell who gave the correct answer, I did not. And also it is impossible to tell how come others have got other answers. I am a student of physics like you, and I obtained second option. So, I hope this solves your problem

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