Question

Two objects of masses \[100{\text{ }}g\] and \[200{\text{ }}g\] are moving along the same line and direction with velocities of $2\,m{s^{ - 1}}$ and $1\,m{s^{ - 1}}$ respectively. They collide and after the collision, the first object moves at a velocity of $1.67\,m{s^{ - 1}}$ . Determine the velocity of the second object.

Answer 1

Hint:When an object ‘A' exerts a force on an object ‘B,' object B replies with a force of equal magnitude but opposite direction, according to Newton's third law. The law of conservation of momentum was derived from this concept by Newton. And in order to answer this question, we will apply this concept to arrive at our desired result.

Complete step by step answer:
Law of conservation of momentum states that- “For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.”Following are the examples of law of conservation of momentum:
-Air-filled balloons
-System of gun and bullet
-Motion of rockets

Given:Mass of first object $\left( {{m_1}} \right) = 100g = 0.1\,kg$
Mass of second object $\left( {{m_2}} \right) = 200g = 0.2\,kg$
Velocity of ${m_1}$ before collision $\left( {{v_1}} \right) = 2\,m{s^{ - 1}}$
Velocity of ${m_2}$ before collision $\left( {{v_2}} \right) = 1\,m{s^{ - 1}}$
Velocity of ${m_1}$ after collision $\left( {{v_3}} \right) = 1.67\,m{s^{ - 1}}$
We have to find out the velocity of ${m_2}$ after collision i.e. ${v_4}$
According to the law of conservation of momentum,
Total momentum before collision = Total momentum after collision
Therefore, ${m_1}{v_1} + {m_2}{v_2} = {m_1}{v_3} + {m_2}{v_4}$
Substituting the above values in the equation
$2(0.1) + 1(0.2) = 1.67(0.1) + {v_4} \times (0.2)$
$\Rightarrow 0.4 = 0.167 + 0.2 \times {v_4}$
$\therefore {v_4} = 1.165\,m{s^{ - 1}}$

Hence, the velocity of ${m_2}$ after collision is $1.165\,m{s^{ - 1}}$.

Note:This law of conservation of momentum is true regardless of how difficult the force between particles is. Similarly, if there are multiple particles, the overall change in momentum is 0 since the momentum exchanged between each pair of particles sums to zero. All interactions, including collisions and separations induced by explosive forces, are subject to this conservation law. It can also be applied to situations where Newton's rules do not apply, such as in relativity theory and electrodynamics.