Jump to content
  • 0

Momentum WA: Billiard Ball Problem


willorn

Question

I'm hoping this is the right place to post for Physics C Problems.

I thought I heard that people were confused by the billiards web assign so I thought I'd weigh in. To me it seems like the velocities of the cue ball and the 8-ball have been switched on the webassign, but maybe I'm crazy. Also, I only know from experience that perfectly spherical billiard balls that collide perfectly tangentially ricochet off each other at complimentary angles, but the mathematical explanation in the answer packet leaves a bit to be explained for me. Any clarification would be much appreciated!

?ui=2&ik=7a84e892b6&view=att&th=12c43537d3d8d013&attid=0.0&disp=inline&zw

  • Like 1
Link to comment
Share on other sites

1 answer to this question

Recommended Posts

  • 0

Some thoughts:

Start off with conservation of energy to relate the velocities, so that:

png.latex? $$v_{ci}^2 = v_{cf}^2 + v_{8b

Note that this is a Pythagorean Theorem relationship, therefore they must form a right triangle, and the angles between png.latex? v_{cf} and png.latex? v_{8ball} must be 90°. You can use this to determine your angles after the collision. A diagram here is helpful.

Next, use conservation of momentum in the x-direction to relate all x-component velocities before and after the collision:

png.latex? $$m{v_{ci}} = m{v_{cf}}\cos {

You can also use conservation of momentum in the y-direction in the same way:

png.latex? $$0 = m{v_{cf}}\sin {\theta _

Solve these equations simultaneously to obtain png.latex? v_{cf} and png.latex? v_{8ball} .

Reminder: Your calculator must be in degree mode!

:egg)

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...