# Billiard ball physics problem

#### Metropolis

Hi guys, I am new here and I am having a LOT of trouble with this new momentum stuff, which I failed in

Here's a question:

A billiard ball has mass 210 g. It's hit with spin and bounces off the side of a table. The initial speed of ball is 1.6 ms-1 (at angle of 60 degrees) and its final speed is 0.8ms-1 (at angle of 30 degrees)

1) Find the change in the momentum of ball due to collision

I had trouble even starting the question. I drew the normal between the collision, and did 90-30=60 to find the inside angle and 90-60=30 for the other. Is anyone able to give me a hint on what formula to use? I'm not familiar with this because I usually do the problems with same initial and final speed.

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#### Doc Al

Mentor
By definition, the change in the linear momentum is
$$m(\vec{v}_f - \vec{v}_i)$$

Hint: Try expressing the velocity vectors in terms of components.

#### Metropolis

Thanks for the tip, I tried using it, and I made up a vector component thing, but I think I am totally wrong

http://img95.imageshack.us/img95/1408/vector4sq.jpg [Broken]

I added 60 and 30, and the angle ended up being 90, so right angle

and I used Pythagoras' theorem, but I think that is not right...like am I supposed to do Vector sum? and find the resultant vector?...it's all so puzzling to me!:tongue2:

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#### Doc Al

Mentor
Close! But instead of adding the vectors you need to subtract them. (Hint: Adding the negative of a vector is equivalent to subtracting it.)

#### Metropolis

Does the inside angle have any relevance?

So is the change in velocity just 1.6 + (-0.8) = 0.8 ?

#### Doc Al

Mentor
Metropolis said:
Does the inside angle have any relevance?
Of course the angle matters.

So is the change in velocity just 1.6 + (-0.8) = 0.8 ?
No! Just redraw your diagram to show the final velocity minus the initial velocity. (These are vectors and must be treated as such.) You are almost there.

Hint: To find the negative of a vector, just flip its direction 180 degrees.

#### Metropolis

I drew this diagram, is it right or not? Does the resultant vector represent the change in velocity or is there more to it than this?

http://img463.imageshack.us/img463/3143/vectordiagram5hh.jpg [Broken]

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#### Doc Al

Mentor
Looks good to me, except that the resultant (the "vertical" arrow) is pointing in the wrong direction.

V is the final velocity; U is the initial velocity. You drew (correctly) V + (-U). Make sure you draw the resultant correctly.

#### Metropolis

Oh! haha duh! I meant to draw the resultant vector pointing the other way!

Anyways, does this mean that the change in velocity is just -0.8? That can't be right..

#### Doc Al

Mentor
Metropolis said:
Anyways, does this mean that the change in velocity is just -0.8? That can't be right..
It's not. Where do you get that conclusion? Find the resultant (just like you did before).

Hint: If the resultant is the hypotenuse of a right triangle, then the Pythagorean theorem applies.

If all you need is the magnitude of the change in momentum, just find the magnitude of the resultant. But if you need the direction as well, you'll need to use a bit of geometry. (Or use components, like I first suggested.)

#### Metropolis

I get confused with this question because I'm referring to other similar problems which don't have a direct right angle

so the change in velocity is 1.789 m.s-1? {from P's theorem}

#### Doc Al

Mentor
Metropolis said:
I get confused with this question because I'm referring to other similar problems which don't have a direct right angle
For those problems, where there's no right angle to make your life easier, use the component method to add/subtract vectors.

so the change in velocity is 1.789 m.s-1? {from P's theorem}
Sounds good to me.

#### Metropolis

Thanks a lot for your help Doc Al!

Now I think I can handle the other parts of the question

EDIT: So for the 2nd part of the question, I have a major problem (I think)...it tells me to find the force the side of table applies to ball...question is...F= Change in momentum / change in time...but I was not given any time data...is it because there's another approach to it? Or did this question that my teacher set have something missing? (which sometimes happens)

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