Calculate Change in Momentum of Billiard Ball | CaptFormal

In summary, to find the magnitude of change in momentum of a billiard ball after striking a cushion, one must calculate the difference in horizontal and vertical components of its initial and final velocities. In this case, the change in horizontal component is -7.8 m/s and the change in vertical component is 0.8779 m/s. Taking the resultant of these components will give the magnitude of change in momentum, which is approximately 7.83 kg·m/s.
  • #1
CaptFormal
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Homework Statement



A billiard ball of mass m = 0.15 kg strikes the cushion of a billiard table at θ1 = 48° and a speed v1 = 21 m/s. It bounces off at an angle of θ2 = 670 and a velocity of v2 = 16 m/s. What is the magnitude of its change in momentum (in kg·m/s)?

http://schubert.tmcc.edu/res/msu/mmp/kap6/picts/pool.gif


Homework Equations





The Attempt at a Solution


Not sure how to solve this one. Any help will be appreciated.


CaptFormal
 
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  • #2
Take the vertical and horizontal components of v1 and v2.
Find the difference in vertical and horizontal components. Take care of signs.Then take the resultant of these components.
 
  • #3
Ok, so here is what I got so far.

Vx = 21cos(48) - 16cos(67) = 7.8

Vy = 21sin(48) - 16sin(67) = 0.8779

Now I am not sure what to do. I tried the following:

(7.8^2 + 0.8779^2)^(1/2)

and then took that answer and multiplied it by the mass but it was incorrect. What am I missing?
 
  • #4
Vx = 21cos(48) - 16cos(67) = 7.8
This is wrong. vx components are in the opposite direction. So the change in vx is
Vx = - 21cos(48) - 16cos(67) = ?
 

1. What is momentum and why is it important in billiards?

Momentum is a measure of the quantity of motion an object has. In billiards, momentum is important because it determines how much force is transferred between the cue ball and object balls when they collide. This helps players predict the direction and speed of the balls after a shot.

2. How do you calculate the change in momentum of a billiard ball?

The change in momentum of a billiard ball can be calculated using the formula: Δp = mΔv, where Δp is the change in momentum, m is the mass of the ball, and Δv is the change in velocity. This formula can help players understand how much force is required to achieve a desired result in a shot.

3. Are there any factors that can affect the change in momentum of a billiard ball?

Yes, there are several factors that can affect the change in momentum of a billiard ball. These include the mass and velocity of the ball, the angle and direction of the shot, and any external forces such as friction or spin.

4. How does the change in momentum of a billiard ball impact the game?

The change in momentum of a billiard ball can greatly impact the game as it determines how the balls will move and interact with each other after a shot. Players must consider the change in momentum in order to make accurate predictions and strategic shots.

5. Can the change in momentum of a billiard ball be manipulated?

Yes, the change in momentum of a billiard ball can be manipulated by adjusting the force and angle of the shot, as well as applying spin to the cue ball. Skilled players are able to manipulate the change in momentum to achieve desired results and improve their game.

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