Question

A student must analyze data collected from an experiment in which a block of mass 2M traveling with a speed v0 collides with a block of mass M that is initially at rest. After the collision, the two blocks stick together. What applications of the equation for the conservation of momentum represent the initial and final momentum of the system for a completely inelastic collision between the blocks?

Answer 1

Solution :

In the question, it is given that the collision is inelastic and the blocks stick together.

In an inelastic collision, the linear momentum is conserved but the kinetic energy is not conserved.

The linear momentum is given by :

$\vec p = m \vec v$ (mass x velocity)

So according to the conservation of linear momentum,

$\vec p_{(\text{before collision})}=\vec p_{(\text{after collision})}$

Let the velocity after the collision is $v_F$

$m_1v_0+m_2 \times 0 = m_1v_F+m_2v_F$

Putting the values of $m_1 \text{ and}\ m_2$

$m_1=2M \text{ and}\ m_2=M$

∴ $2Mv_0=2Mv_F+Mv_F$, as the blocks stick together after the collision.

and  $2MV_0=3Mv_F$, as the blocks stick together after the collision.