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Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate...

Question:

Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Initially ball A is moving upward along the y axis at 2.0 m/s and ball B is moving to the right along the x axis with speed 3.7 m/s. After the collision ball B is moving along the positive y axis. What is the speed of ball A and B after the collision? What is the direction of motion of ball A after the collision? What is the total momentum and kinetic energy of the two balls after the collision?

Conservation of Momentum

Momentum of a body is given by the product of the mass of the body and the velocity of the body.

Mathematically,

{eq}\displaystyle \vec{P}\ =\ m\ \times\ \vec{v}\\ {/eq}

where:

  • m is the mass of the body
  • {eq}\vec{P} {/eq} is the momentum of the body
  • {eq}\vec{v} {/eq} is the velocity of the body

Now when a system undergoes a process in which there is no net force on the system is acting in a particular direction then the total momentum of the system in that direction is conserved.

If a system of two bodies is going under a collision under the influence of no any external force then the total momentum will be conserved.

Mathematically,

{eq}\displaystyle m_a \vec{v_{ai}}\ +\ m_b \vec{v_{bi}}\ =\ m_a \vec{v_{af}}\ +\ m_b \vec{v_{bf}} {/eq}

where:

  • {eq}m_a\ and\ m_b {/eq} are the masses of the bodies
  • {eq}\displaystyle \vec{v_{ai}}\ and\ \vec{v_{af}} {/eq} are the initial and final velocities of the body A respectively.
  • {eq}\displaystyle \vec{v_{bi}}\ and\ \vec{v_{bf}} {/eq} are the initial and final velocities of the body B respectively.

Answer and Explanation:

Let the mass of the two balls each is equal to {eq}m\ kg {/eq}

Then the momentum of the system before the collision is equal to

{eq}\vec{P_i}\ =\...

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Practice Applying Conservation of Linear Momentum

from Physics 111: Physics I

Chapter 9 / Lesson 3
754

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