Question

A 10kg mass going 4m/s to the right hits a 6kg object going 2m/s left. The 10kg ends up going 0.5 m/s left.

A) find the velocity of the 6kg object afterwards
B) was the collision elastic or inelastic?​

Answer 1

a) 5.5 m/s

b) elastic

Step-by-step explanation:

a) This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
`p_(i)` must be equal to the final momentum
`p_(f)`:

`p_(i)=p_(f)` (1)

Where:

`p_(i)=MV_(o)+mU_(o)` (2)

`p_(f)=MV_(f)+mU_(f)` (3)

`M=10 kg` is the first mass

`V_(o)=4 m/s` is the initial velocity of th first mass, to the right

`m=6 kg` is the second mass

`U_(o)=-2 m/s` is the initial velocity of the second mass, to the left

`V_(f)=-0.5 m/s` is the final velocity of the first ball

`U_(f)` is the final velocity of the seond ball

Then:

`MV_(o)+mU_(o)=MV_(f)+mU_(f)` (4)

Finding
`U_(f)`:

`U_(f)=(M(V_(o)-V_(f))+mU_(o))/(m)` (5)

`U_(f)=(10 kg (4 m/s-(-0.5 m/s))+(6 kg)(-2m/s))/(6 kg)` (6)

`U_(f)=5.5 m/s` (7) This is the velocity of the second mass, to the right

b) According to the description of the problem, this is an elastic collision, because both the total kinetic energy of the system and the linear momentum are conserved. That is, during the collision there is no sound, heat or permanent deformations in the bodies as a result of the impact.