# Is Ignoring the Y-Component in Billiard Ball Collision Calculations Correct?

• aatari
In summary, the conversation is about a physics problem where a cue ball collides with a stationary billiard ball. The cue ball deflects at an angle of 30 degrees and the question is to calculate the original speed of the cue ball if the billiard ball ends up traveling at a certain speed. The solution being discussed includes the use of the equation Pi = Pf, but there is uncertainty about whether the y-component of the cue ball's velocity needs to be incorporated into the solution. The conversation ends with a question about the direction of the billiard ball after the collision.
aatari
Could someone please have a look at my solution and tell me if it makes sense. Although I am able to get the initial velocity that the question asked for, however the fact that I did not incorporate the y-component which is 1.2sin30 degrees into the solution makes me doubtful. If I do need to use that into the solution, how would that fit in? Please help!

1. Homework Statement

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up traveling at 1.6 m/s.

Pi = Pf

## The Attempt at a Solution

[/B]

aatari said:
Could someone please have a look at my solution and tell me if it makes sense. Although I am able to get the initial velocity that the question asked for, however the fact that I did not incorporate the y-component which is 1.2sin30 degrees into the solution makes me doubtful. If I do need to use that into the solution, how would that fit in? Please help!

1. Homework Statement

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up traveling at 1.6 m/s.

Pi = Pf

## The Attempt at a Solution

View attachment 213143
[/B]
In what direction do you think the second ball will go?

## 1. How do collisions between billiard balls work?

When two billiard balls collide, they exert equal and opposite forces on each other. This is known as Newton's Third Law of Motion. The force of the collision depends on the masses and velocities of the two balls. The direction and speed of each ball after the collision can be calculated using the principles of conservation of momentum and energy.

## 2. Why do billiard balls have different "numbers" on them?

The numbers on billiard balls are used for identification and positioning during gameplay. These numbers are also used to keep track of points and fouls. The numbers are typically assigned in a specific order to the balls, with the cue ball being numbered 1 and the other balls numbered sequentially in a clockwise direction.

## 3. What happens when the cue ball collides with another ball?

When the cue ball collides with another ball, it transfers some of its energy and momentum to the other ball. This causes the other ball to move in a different direction and at a different speed. The amount of energy transferred depends on the angle and speed of the cue ball, as well as the mass and initial velocity of the other ball.

## 4. Can collisions between billiard balls be perfectly elastic?

In theory, collisions between billiard balls can be perfectly elastic, meaning that no kinetic energy is lost during the collision. However, in reality, there is always some amount of energy lost due to friction between the balls and the table surface. This is why billiard balls eventually come to a stop, even on a perfectly smooth surface.

## 5. How do collisions between billiard balls differ from other types of collisions?

Collisions between billiard balls differ from other types of collisions in that they are usually elastic, meaning that the total kinetic energy of the system is conserved. This is due to the hardness and smoothness of the billiard balls, which allows for minimal energy loss during collisions. Additionally, billiard balls are usually considered to be point masses, meaning that their size and shape do not affect the outcome of the collision.

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