What is the final speed of a mass collision?

[ola_12]

Homework Statement

two objects, each moving with the same speed but opposite directions, collide head on. after collision smaller object of mass
= 100g embedded in large object mass= 500g. What is the final speed of the combined object in terms of initial speed of the two objects?

Relevant Equations

conservation of momentum

I am stuck, please help. I did the conservation part but then i can't move on.

 

[Greg Bernhardt]

I am stuck, please help. I did the conservation part but then i can't move on.

Please show this part you've done.

 

[ola_12]

m1Vi1 + m2Vi2 = m1Vf2 + m2Vf2
Vf = Vi(m1-m2) / (m1+m2)
this is how i interpreted it, I'm not sure if I'm on the right track or not.

 

[jcloo]

Looks good! Now you can reduce the equation by using the fact that m2 is equal to 5*m1.

 

[SammyS]

m1Vi1 + m2Vi2 = m1Vf2 + m2Vf2
Vf = Vi(m1-m2) / (m1+m2)
this is how i interpreted it, I'm not sure if I'm on the right track or not.

Yes, that will give the speed of the combined object assuming that m₁ > m₂ .

 

[ola_12]

No, I think you've lost me guys, I'm not sure I'm getting what y'all mean about m2 = 5*m1. what about the initial velocity that we don't have? Cause when i substitute m2 I still can't get Vf.

 

[jcloo]

No, I think you've lost me guys, I'm not sure I'm getting what y'all mean about m2 = 5*m1. what about the initial velocity that we don't have? Cause when i substitute m2 I still can't get Vf.

The smaller mass m1 is 100 grams while the larger mass m2 is 500 grams. This means that m2=5*m1. We can use this fact to place it in the equation that you found earlier to find the final speed Vf in terms of the initial speed Vi.

 

[ola_12]

oh I see now, thank you everyone :)