Question

Assuming that no outside forces are acting on ma or mb, which of the following expression BEST represents the speed, v' of the masses after the collision?

​

Answer 1

Answer: B

Step-by-step explanation:

The conservation of momentum states that the initial momentum of the system must equal the final momentum of the system. Our system in this case is the two colliding objects and ONLY the two colliding objects. Initially, our system had mass 1 moving towards a stationary mass 2. The stationary mass has a velocity of 0m/s and therefore has no momentum. The initial momentum would then be:

`p_i=m_1v_1_i+m_2v_2_i`

`p_i=m_1v_1_i`

The final momentum depends on what type of collision occurred. This case is the simplest type of collision, when the objects stick to each other and act as one. Since the objects move together, their velocity must be the exact same. Our final momentum looks like:

`p_f=m_1v_f+m_2v_f`

`p_f=v_f(m_1+m_2)`

Setting the initial momentum equal to the final momentum:

`p_i=p_f`

`m_1v_1_i=v_f(m_1+m_2)`

Solving the final velocity:

`v_f=m_1v_1_i/(m_1+m_2)`

Which matches answer B