What is an example of a perfectly elastic collision? A perfectly elastic collision is a type of collision in which both kinetic energy and momentum are conserved. In other words, the total amount of energy and momentum before the collision is equal to the total amount of energy and momentum after the collision. This type of collision is often referred to as a “bounce-back” collision because the objects involved in the collision will return to their original positions after the collision. In this article, we will explore a real-life example of a perfectly elastic collision and discuss its implications in the physical world.
In the physical world, a common example of a perfectly elastic collision is the collision between two billiard balls. When two billiard balls collide, they bounce off each other without any loss of energy. This is because the balls are made of hard materials that do not deform during the collision, and the collision is perfectly elastic. The following equation can be used to describe the conservation of momentum and kinetic energy in a perfectly elastic collision:
m1 v1i + m2 v2i = m1 v1f + m2 v2f
(1/2) m1 v1i^2 + (1/2) m2 v2i^2 = (1/2) m1 v1f^2 + (1/2) m2 v2f^2
where m1 and m2 are the masses of the two billiard balls, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.
Let’s consider a scenario where two billiard balls, Ball A and Ball B, are moving towards each other with equal but opposite velocities. Ball A has a mass of 0.5 kg and an initial velocity of 2 m/s, while Ball B has a mass of 0.5 kg and an initial velocity of -2 m/s. When the balls collide, they will bounce off each other with the same velocities but in opposite directions.
Using the conservation of momentum equation, we can determine the final velocities of the balls:
0.5 kg 2 m/s + 0.5 kg (-2 m/s) = 0.5 kg v1f + 0.5 kg v2f
1 kg m/s = 0.5 kg v1f + 0.5 kg v2f
2 m/s = v1f + v2f
Using the conservation of kinetic energy equation, we can determine the final velocities of the balls:
(1/2) 0.5 kg (2 m/s)^2 + (1/2) 0.5 kg (-2 m/s)^2 = (1/2) 0.5 kg v1f^2 + (1/2) 0.5 kg v2f^2
1 J = 0.25 kg v1f^2 + 0.25 kg v2f^2
4 J = v1f^2 + v2f^2
Since the balls have equal masses and the initial velocities are equal but opposite, we can conclude that the final velocities will also be equal but opposite. Therefore, we can set v1f = -v2f:
4 J = v1f^2 + (-v1f)^2
4 J = 2 v1f^2
2 J = v1f^2
v1f = √(2 J / 0.5 kg)
v1f = √(4 m^2/s^2)
v1f = 2 m/s
Since v1f = -v2f, we can conclude that v2f = -2 m/s.
In conclusion, a perfectly elastic collision is a type of collision in which both kinetic energy and momentum are conserved. The collision between two billiard balls is a real-life example of a perfectly elastic collision. When two billiard balls collide, they bounce off each other without any loss of energy, demonstrating the conservation of momentum and kinetic energy. This example highlights the importance of understanding the principles of perfectly elastic collisions in various fields of physics and engineering.
