Kinetic energy transformed in a collision involving coalescing particles

[greg_rack]

Homework Statement

A particle of mass m has kinetic energy E when it collides with a stationary particle of mass M . The two particles coalesce.
Which of the following expressions gives the total kinetic energy transferred to other forms of energy in the collision?

Relevant Equations

Kinetic energy
Energy conservation

This problem got me kinda confused since I cannot really understand the question... who tells me how the energy dissipated in this case? Has it all transformed into heat to cause the coalesce of the two particles, or ar the two particles now merged together still traveling with a certain amount of kinetic energy?

 

[PeroK]

Homework Statement:: A particle of mass m has kinetic energy E when it collides with a stationary particle of mass M . The two particles coalesce.
Which of the following expressions gives the total kinetic energy transferred to other forms of energy in the collision?
Relevant Equations:: Kinetic energy
Energy conservation

This problem got me kinda confused since I cannot really understand the question... who tells me how the energy dissipated in this case? Has it all transformed into heat to cause the coalesce of the two particles, or ar the two particles now merged together still traveling with a certain amount of kinetic energy?

Momentum is conserved. Does that help?

 

[greg_rack]

Momentum is conserved. Does that help?

Right, but I'm still stuck... don't I need a final velocity? And how does momentum relates to energy?

 

[PeroK]

Right, but I'm still stuck... don't I need a final velocity? And how does momentum relates to energy?

What does the momentum conservation equation tell you?

 

[greg_rack]

What does the momentum conservation equation tell you?

m_1iv_1i+m_2iv_2i=m_1fv_1f+m_2fv_2f
In that case, since the two coalesce, there will be only one final velocity

 

[PeroK]

m_1iv_1i+m_2iv_2i=m_1fv_1f+m_2fv_2f

Okay, but the point of that equation isn't to quote it. It's to apply that equation to each specific problem.

 

[greg_rack]

Okay, but the point of that equation isn't to quote it. It's to apply that equation to each specific problem.

In this case: mv_1initial=v_final(M+m)
And how does this relate to the "total kinetic energy transferred to other forms of energy in the collision"?

 

[PeroK]

In this case: mv_1initial=v_final(M+m)
And how does this relate to the "total kinetic energy transferred to other forms of energy in the collision"?

Does that not give you the final velocity you were asking for?

 

[PeroK]

Now the point is: what are we looking for? That's not clear to me, since how could we know in which other forms was the energy transformed? I don't know if you got what point I'm missing... its difficult to express some concepts in English :)

All they want is the kinetic energy that is lost: $KE_i - KE_f$.

 

[greg_rack]

All they want is the kinetic energy that is lost: $KE_i - KE_f$.

Finally got it! So:
½mv₁²-½(M+m)((mv₁)²/(M+m)²)

EDIT: and it works... thank you, I'm crying!