Two small, identical steel balls collide completely...

Two small, identical steel balls collide completely elastically. Initially ball 1 is moving with velocity $v_{1}$, and ball 2 is stationary. After the collision, the final velocities of ball 1 and ball 2 are A. $12 \mathrm{v} 1 ; 12 \mathrm{v} 1 \frac{1}{2} v_{1} ; \frac{1}{2} v_{1}$ B. $v_{1} ; 2 v_{1}$ C. $0 ; v_{1}$ D. $-v_{1}$; 0 E. $-v_{1} ; 2 v_{1}$

Two small, identical steel balls collide completely elastically. Initially ball 1 is moving with velocity $v_{1}$, and ball 2 is stationary. After the collision, the final velocities of ball 1 and ball 2 are
A. $12 \mathrm{v} 1 ; 12 \mathrm{v} 1 \frac{1}{2} v_{1} ; \frac{1}{2} v_{1}$
B. $v_{1} ; 2 v_{1}$
C. $0 ; v_{1}$
D. $-v_{1}$; 0
E. $-v_{1} ; 2 v_{1}$

Key Concepts

Conservation of Momentum

The conservation of momentum principle states that the total momentum of a closed system remains constant before and after a collision. In the context of collision problems, this allows for the analysis of how the momenta of individual objects are redistributed upon impact.

Conservation of Kinetic Energy

In elastic collisions, kinetic energy is conserved in addition to momentum. This conservation provides a second equation that can be used to determine the final velocities of the colliding objects, making it possible to solve for unknown variables in collision problems.

Elastic Collision

An elastic collision is a type of collision where both momentum and kinetic energy are conserved. This principle is fundamental in problems involving the motion of colliding bodies, and it specifically applies when no energy is lost to sound, heat, or deformation during the impact.

Collision of Identical Masses

When two identical masses undergo a one-dimensional elastic collision, the outcome is typically such that the moving mass transfers its velocity to the stationary mass. This results in the moving mass coming to rest post-collision while the stationary mass moves with the initial velocity of the first mass.

Transcript

00:02 Hi, this question we're given that two identical steel balls collide.

00:06 So that means they have the same mass.

00:07 So the first steel ball comes in this direction.

00:10 It's velocity of v1 and has a mass of m.

00:17 And the second steel ball is stationary.

00:19 So the velocity is zero.

00:21 The mass is also m.

00:24 And when they collide, i want to find the final velocities of ball 1.

00:28 So this ball 1 is ball 2.

00:32 So i'm also i'm also that collision is perfectly elastic.

00:36 So that means that.

00:37 Both momentum and kinetic energy are conserved.

00:41 So for momentum, we can solve the conservation and p is equal to mv.

00:48 P is momentum, m is the mass, v's the velocity.

00:52 So the total initial momentum is equal to the total final momentum.

00:56 So multiply the mass times the initial velocity of the first ball, i'm added to the mass and the initial velocity of the second ball, and that will be equal to the sum of the products of the mass and the final velocities of the first ball.

01:10 The two balls so for the initial we have m v1 plus mass time is zero and for the final we have let's call the final velocities of the first ball vf one one of the second ball we have two so this mvf one plus m vf two m we can cancel our m on on both sides of v1 is equal to vf one plus vf two next you can express the conservation of kinetic energy...

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