Question

Two objects each of mass 1.5 kg, are moving in the same straight line but in opposite directions. Velocity of each object is $2.5\text{ m}{{\text{s}}^{-1}}$before collision during which they stick together. What will be the velocity of the combined object after the collision?
A.)0 m/s
B.)3.75 m/s
C.)0.75 m/s
D.)3 m/s

Answer 1

Hint: There are two types of collisions, one is elastic collision and another one is an inelastic collision. In this case, the collision is inelastic because after the collision the two bodies stick together.

Complete step by step answer:
So we have two bodies of an equal mass of 1.5 kg and moving with an equal velocity of $2.5\text{ m}{{\text{s}}^{-1}}$ in the opposite direction. So the direction from left to right is taken as positive while the direction from right to left is taken as negative. So the momentum is conserved in the case of an inelastic collision.

So the momentum of the first body of mass ${{\text{m}}_{\text{1}}}$=1.5 kg and moving with a velocity ${{\text{v}}_{\text{1}}}$=$2.5\text{ m}{{\text{s}}^{-1}}$is given by , ${{\text{P}}_{\text{1}}}={{\text{m}}_{\text{1}}}{{\text{v}}_{\text{1}}}$ which is equal to $3.75\text{ kgm}{{\text{s}}^{-1}}$.

Since the mass and velocity of the second body is same as the mass and the velocity of the first body, the magnitude of momentum of the second body $\left( {{\text{P}}_{2}} \right)$ will be equal to the first body’s momentum$\left( {{\text{P}}_{\text{1}}} \right)$. But since the directions of motion are opposite to each other the second body’s momentum will have a negative sign.

$\therefore \left( {{\text{P}}_{2}} \right)=-\left( {{\text{P}}_{\text{1}}} \right)$……equation (1)
So suppose after the collision the combined body moves with a velocity V and has a mass M, where M=${{\text{m}}_{\text{1}}}+{{\text{m}}_{\text{2}}}$. So according to the law of conservation of momentum the initial momentum before collision should be equal to final momentum after collision.

$\begin{align}
  & \text{Initial Momentum}=\text{Final Momentum} \\
 & {{\text{P}}_{1}}+{{\text{P}}_{\text{2}}}=\text{P=MV} \\
\end{align}$

Substituting equation (1) in above equation we get,

${{\text{P}}_{1}}+(-{{\text{P}}_{1}})=\text{MV}$
$\therefore \text{V}=0\text{ m/s}$

Which means that the two bodies after collision will be combined together and will be at rest. They will not be moving.

So the answer to the Question is option (A)- 0 m/s.

Note: In an elastic collision both the kinetic energy and momentum associated with the system is conserved.
In an inelastic collision only momentum of the system is being conserved.
The formal definition of collision is, “A collision is an event in which two or more bodies exert forces on each other in about a relatively short time.”