Question

Two objects, each of mass $1.5\mathrm{kg}$, are moving in the same straight line but in opposite directions. The velocity of each object is $2.5\mathrm{m}/\mathrm{s}$ before the collision during which they stick together. What will be the velocity of the combined object after collision?

Answer 1

Step 1: Conservation of momentum

1. Conservation of momentum states that the momentum of the whole system remains constant at any instant.
2. The momentum of the whole system before collision will be the same after the collision.
3. Momentum can be calculated by multiplying the mass of the object by its velocity.

The equation for the momentum can be written by equating the total momentum of the system before and after the collision as follows:

$$\begin{gathered} m_1{u}_1+m_2{u}_2=\left(m_1+m_2\right)v \\ \left(1.5\mathrm{kg}\times 2.5\mathrm{m}/\mathrm{s}\right)+\left\{1.5\mathrm{kg}\times \left(-2.5\mathrm{m}/\mathrm{s}\right)\right\}=\left(1.5\mathrm{kg}+1.5\mathrm{kg}\right)v \end{gathered}$$

Here,

$m_1$ and $m_2$ are the masses of the objects.

$u_1$ and $u_2$ are the velocities of the object before the collision.

$v$ is the velocity of the whole object after the collision.

Since the second object is moving in the opposite direction, the velocity is considered negative for the second object.

Step 2: Calculation of the velocity of the object after the collision.

Simplifying the equation to calculate the final velocity of the object after the collision.

$$\begin{gathered} 0\mathrm{kg}-\mathrm{m}/\mathrm{s}=3\mathrm{kg}\times \mathrm{v} \\ \mathrm{v}=0\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the velocity of the combined object after the collision is $0\mathrm{m}/\mathrm{s}$.