Physics Question?

Question

Two balls are approaching each other for a head on collision. Ball #1 has a velocity of 8.9 m/sec and Ball #2 has a velocity of -11 m/sec.

Part A.) What is the velocity of the center of the two ball if they both have the same mass?

Part B.) What is the velocity of the center of the mass of the two balls if the mass of Ball #1 is 4 times as big as the mass of Ball #2 ?

Answer 1

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 = [(8.9 - 11) / (2)] [ i ] = - 1.05 i m/s

that is CM will move towards the -ve x-axis or will be influenced by B-ball

b) m1= 4m2

Vcm = (4 v1 - v2) / (4+1) [ i ]

= [(35.6 - 11) / (52) ] [ i ] = 4.92 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

Answer 2

The velocity of the center OF MASS is the total momentum divided by the total mass.

(m1 v1 + m2 v2) / (m1 + m2)

That equation will suffice for parts A and B.