Three masses are moving along the x-axis.Their masses and velocities are m₁ = m with v₁ = v,m₂ = 2m with v₂ = 2v,and m₃ = 3m with v₃ = -3v (the minus sign indicating this velocity is in the negative x-direction).The three masses collide and stick together in a completely inelastic collision.What is the resultant velocity of the combined mass? A)0,since their combined momentum is zero. B)-2v/3 C)14v/3 D)-v

Question

Quizplus · Accepted Answer

Before the collision, the total momentum of the system is:

p = m1v1 + m2v2 + m3v3
p = m v + 2m (2v) + 3m (-3v)
p = -7mv

Since the collision is completely inelastic, the total mass of the system after the collision is:

M = m1 + m2 + m3
M = m + 2m + 3m
M = 6m

The resultant velocity of the combined mass can be found using the conservation of momentum:

p = Mv'

where v' is the resultant velocity of the combined mass.

Substituting the values, we get:

-7mv = 6m v'
v' = -7/6 v

Therefore, the resultant velocity of the combined mass is -7/6 times the velocity of the leftmost mass, which is -2v/3. Hence, the answer is B.

Three Masses Are Moving Along the X-Axis