inellastic collisions and velocity

Question

a 5 kg box with a velocity of 10m/s will attach inelastically to a 5 kg box and then both boxes will attach to a 5kg box which has a velocity of 5m/s to the left. what is the end velocity

Answer 1

I am assuming the initial 10 m/s is to the right, which I define as (+) direction, and left as (-) direction.  Let us do this step by step.

 

m1, m2, and m3 = 5 kg

 

Collision of m1 with m2:

 

v1 = 10 m/s, v2 = 0

 

Momentum is still conserved even though the collision is inelastic:

 

Initial momentum: pi = m1*v1

Final momentum after collision:  pf = (m1 + m2)*v = pi = m1*v1

v = m1*v1 / (m1 + m2) = (5)(10) / (5 + 5) m/s = 50/10 m/s = 5 m/s

 

Collision of (m1 + m2) moving at speed v = 5 m/s with m3 moving at speed -5 m/s:

 

Momentum is still conserved.

 

Initial momentum: (m1 + m2)*v + m3*v3 (where v3 = -5 m/s)

Final momentum:  (m1 + m2 + m3)*vf, where vf = final speed

 

(m1 + m2)*v + m3*v3 = (m1 + m2 + m3)*vf

 

vf = [(m1 + m2)*v + m3*v3] / (m1 + m2 + m3) = [(5 + 5)*(5) + (5)(-5)] / (5 + 5 + 5) m/s

 

vf = (50 - 25) / 15 m/s = 25/15 m/s = 1.67 m/s (to the right)