# Homework Help: Billiard ball physics problem

1. Mar 24, 2006

### 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.

2. Mar 24, 2006

### Staff: 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.

3. Mar 24, 2006

### 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:

Last edited by a moderator: May 2, 2017
4. Mar 24, 2006

### Staff: 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.)

5. Mar 24, 2006

### Metropolis

Does the inside angle have any relevance?

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

6. Mar 24, 2006

### Staff: Mentor

Of course the angle matters.

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.

7. Mar 24, 2006

### 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]

Last edited by a moderator: May 2, 2017
8. Mar 24, 2006

### Staff: 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.

9. Mar 24, 2006

### 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..

10. Mar 24, 2006

### Staff: Mentor

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.)

11. Mar 24, 2006

### 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}

12. Mar 24, 2006

### Staff: Mentor

For those problems, where there's no right angle to make your life easier, use the component method to add/subtract vectors.

Sounds good to me.

13. Mar 24, 2006

### 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)

Last edited: Mar 25, 2006