Question

Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 210 g, remains at rest. (a) What is the mass (in g) of the other sphere?
(b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 1.6 m/s?

Answer 1

(mu)before=(mu)after

Answer 2

because itselastic collision

Answer 3

mu?
\[\mu ?\]
That is coefficient of static friction...

Answer 4

no no mass

Answer 5

its conservation of momentum

Answer 6

Ok so first of all lets reason this problem. We know tha the mass of sphere B (the other sphere) is much bigger than A since A stopped. Noe lets state the equations. There is the equation of energy and the equation of momentum:\[E _{i}=E _{f}\rightarrow \frac{ 1 }{ 2 }m _{A}v _{i} ^{2}+\frac{ 1 }{ 2 }m _{B}v _{i} ^{2}=\frac{ 1 }{ 2 }m _{B}v _{f }^{2}\]\[p _{i}=p _{f} \rightarrow m _{A} v _{i}-m _{B}v _{i}=m _{B}v _{f}\]Remember that in the momentum equation you need a minus sign since v is velocity and therfore has a direction. Now you have three incognitas, but if you work through the math one of them should cancel. Have you done the maths or do you want me to show you?

Answer 7

I will just show since I love this things :):

First of all you need to simplify the final velocity in the momentum equation:\[m _{A}v _{i}-m _{B}v _{i}=m _{B}v _{f}\rightarrow v _{f}=v _{i}\frac{ m _{A}-m _{B} }{ m _{B} }\]Then you replace it in the energy equation. The trick is then to cancel of the initial velocities you are left with along with the halfs.\[\frac{ 1 }{ 2 }m _{A}v _{ i}^{2}+\frac{ 1 }{2 }m _{B}v _{i}^{2}=\frac{ 1 }{ 2 }m _{B}v _{i}^{2}\frac{ (m _{A}-m _{B})^{2} }{ m _{B}^{2} }\rightarrow m _{A}+m _{B}=\frac{(m _{A}-m _{B})^{2} }{ m _{B} }\]Now if yous solve for the mass of sphere B you get:\[m _{B}=\frac{ 1 }{ 3 }m _{A}\]I have never seen a question like the second one, but ill give it a thought and tell you if I find an answer.

Answer 8

Awesome, it is correct... but I have no clue how to even begin go go about the second part.

Answer 9

Well I gave it a thought and actually the velocity of both masses in frame of reference of the center of mass has to stay the same but in oposite directions (because of some hard maths). Which means that the center of mass must have a velocity of 1.6m/s if one of the spheres remained static.

Answer 10

Wait!!!!!!

Answer 11

You see to find the center of mass you use this equation which if you take the derivative you get velocity and if you solve for the velocity of the center of mass you get the answer:\[(m _{A}+m _{B})r _{cm}=m _{A}r _{A}+m _{B}r _{B} \rightarrow r _{cm}=\frac{ m _{A}r _{A}+m _{B}r _{B} }{ m _{A}+m _{B}} \]\[v _{cm}=\frac{ m _{A}v _{A}+m _{B}v _{B} }{ m _{A}+m _{B}} \]