Two balls are approaching each other for a head on collision. Ball #1 has a velo
ID: 1261644 • Letter: T
Question
Two balls are approaching each other for a head on collision. Ball #1 has a velocity of 9.1 m/sec and Ball #2 has a velocity of -9.4 m/sec.
Just need help with #2
1)
What is the velocity of the center of mass of the two balls if they both have the same mass?
vCOM=
m/sec
Your submissions:
-.15
Computed value:
-.15
Submitted:
Saturday, March 21 at 8:43 PM
Feedback:
Right answer !
2)
What is the velocity of the center of mass of the two balls if the mass of Ball #1 is 3 times as big as the mass of Ball #2?
vCOM=
m/s
Explanation / Answer
Answer: I had done such C of M questions long long back
capitals denote vectors. The position vector of Centre of mass in terms of 2 mass system is given by
Rcm = (m1 r1 + m2 r2) / (m1+m2) [ i ]
[ i ] is the unit vector along positive x-axis
when moving antiparallel - heads-on
Vcm = (m1 v1 - m2 v2) / (m1+m2) [ i ]
a) m1=m2
Vcm = [(9.1 - 9.4) / (2)] [ i ] = - 0.15 i m/s
that is CM will move towards the -ve x-axis or will be influenced by B-ball
b) m1= 3m2
Vcm = (3 v1 - v2) / (3+1) [ i ]
= [(27.3 - 9.4) / (4) ] [ i ] = 4.475 i m/s
that is CM will move towards +ve x-axis or will be influenced by A-ball. The momentum of A-ball will dominate the velocity of CM