Knowing More on Application of Law of Conservation of Momentum

Every object that undergoes a motion has momentum. The object’s mass and speed determine the momentum of the object. The law of conservation of momentum states that any object will have constant momentum before and after the motion.

For example, when two bodies collide, the momentum before the collision is the same as the momentum after the collision. In the above case, we assume that there was no momentum change due to any external forces like friction, air resistance or tension. Some of the best applications of the law of conservation of momentum are as follows-

1. Newton’s cradle: Newton’s cradle is one of the best applications of the law of conservation of momentum. It is a device consisting of swinging sphere balls. When we lift a sphere ball at one of the ends and release it, the sphere ball gains momentum and hits the other balls in the device. Soon the sphere ball at the other end is pushed by the middle balls and further lifted upward. Newton’s cradle is a perfect demonstration of the law of conservation of momentum because if you notice carefully, the number of balls lifted and released from one end will always be equal to the number of balls that rise or move upward from the other end. You will never notice inconsistency because the momentum is conserved. 

2. Air escaping the balloon: When we inflate a balloon, the pressure builds inside, and it gets compressed once we tie a knot to the balloon. After the balloon is released, it flies forward in a direction opposite to the air leaving the balloon. The balloon acquires motion due to the air being released in the opposite direction. The momentum of the air being released is equal to the motion of the balloon, and hence momentum is conserved.

3. Billiard balls and their collisions: When we hit a ball by the stick, the ball collides with the other balls in its path of motion. The momentum from the stick transfers to the ball and then to the other balls in its path. Overall, the momentum in every step of this game remains constant, even during a move. This proves the law of momentum conservation.

Law of conservation of momentum formula

When two balls B1 and B2 collide in an isolated system, the momentum that ball B1 loses is gained by ball B2, and vice versa. Hence, the net momentum in this isolated system remains conserved, and we observe no change in the momentum.

The conservation of momentum formula is: m1v1 + m2v2 = m1v1 + m2v2

In the above formula, the left-hand side (LHS) denotes the total momentum before the collision, and the right-hand side (RHS) denotes the total momentum after the collision.

Conservation of momentum examples with solutions

Example: A boy is running at a velocity of 2m/s to the right side. He jumps onto a trolley at rest. What is the speed of the trolley? What is the speed of the body after he has jumped in?

(weight of the boy→ 35Kg, mass of trolley→ 70 Kg)

Solution: The interaction between the two items takes place when the boy jumps on the trolley.

v1i→ velocity of the boy 

v2i→ velocity of the trolley before the body jumps in it

v1i = 2 and v2i = 0

Before the jump: Momentum P of the boy and trolley system together is,

P = moment of boy + moment of trolley = 35 × 2 + 70 × 0 = 70 Kg m/s

v→ velocity of the trolley (with the boy in it),

Therefore, momentum of the trolley is: Pt = (35 + 70) v

70 = (35 + 70) v             (momentum1 = momentum2)

 v = 70 / 105 = 0.7 m/s to the right.

Example: Two vehicles are colliding, and both are travelling at the same speed of 5ms-1. The weight of the vehicles is 3 kg and 2 kg, respectively. What is the velocity of the trolley after they collide?

Solution: Initial momentum = Final momentum

                      m1v1 + m2v2 = m3v3

        {3×5} + {2×(-5)} = {3+2}v3

                         15 + (-10) = 5v3

                                      v = 5/5

                                      v = 1ms-1

Conclusion

The applications of conservation of momentum given in the section above help us to understand the transfer of momentum and its constant nature throughout a motion in an isolated system. Newton’s cradle is the device that makes us visually observe the transfer of momentum from the first ball to the last ball in the device. The formula for conservation of momentum can be used to find out the velocity and mass of the objects under study and also find the initial or final momentum.