Calculate Change in Momentum of Billiard Ball | CaptFormal

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Homework Help Overview

The problem involves calculating the change in momentum of a billiard ball after it strikes a cushion at a specific angle and speed, then bounces off at a different angle and speed. The subject area pertains to momentum and vector components in physics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss breaking down the velocities into horizontal and vertical components and calculating the differences. There is uncertainty about the signs of these components and how they affect the overall calculation of momentum change.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting the calculation of vector components. However, there is a lack of consensus on the correct signs for the components, leading to confusion in the calculations. The discussion is ongoing with attempts to clarify these points.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding the vector nature of momentum changes.

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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
 
Last edited by a moderator:
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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.
 
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?
 
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) = ?
 

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