Question

A system consisting of two objects has a total momentum of (16 kgm/sec)i and its centre of mass has the velocity of (2 m/s)i.One of the object has the mass 5 kg and velocity (1.6 m/s)i. The mass and velocity of the other objects?

 

Answer 1

Velocity of the center of mass = (2 m/s)=Vcm

 

Mass of one object=5 kg 

Total momentum =Total mass X× velocity of the center of mass   

M=m1+m2

 

16 kgm/sec)i = (m+ 5) × (2 m/s)i  

2m+10=16, m=6/2 

m2=3 kg m1= 5kg

 

 

Velocity of this object=(1.6 m/s)

Now Vcm=(m1v1+m2v2)/(m1+m2)

2=(5 ×1.6 + 3 × v2)/(5+3)

 

2 = (8 + 3v2) /8

16 = 8 + 3v2

 

3v2 = 8

V2=8/2

V2=2.67m/s

 

Total momentum =Total mass X× velocity of the center of mass 

 

Now Vcm=(m1v1+m2v2)/(m1+m2)