Is this correct- momentum question

1. Oct 31, 2007

klm

A 20 g ball of clay traveling east at 2.0m/s collides with a 30 g ball of clay traveling 30 degree south of west at 1.0m/s.
What are the speed of the resulting 50 g blob of clay?

so this is what i i did:

mivi=mfvf
vx= (.02)(2) / (.05) = .8
vy= (.03)(-1)/ .05 = -.6

is that much correct so far? and then i can use vy= v sin theta to find v?

2. Oct 31, 2007

mjsd

hard to understand what you have done with your notations.
but this is clearly a conservation of momentum question. so remember this is a 2D problem, so both total momentun in x and y direction must be the same before and after.

3. Oct 31, 2007

klm

sorry for the messy calculations!

i am basically finding the Vx = ( mass of ball 1)( velocity of ball 1) / ( total mass )
so Vx = ( 0.02 kg) ( 2 m/s ) / ( 0.05 kg ) = 0.8

and Vy = (.03 kg) ( -1 m/s) / (.05 kg) = -.6
(is the bold part in this equation correct? )
but i am a little confused if i can use this equation to find V now, Vy= v sin(theta)

4. Oct 31, 2007

mjsd

As far as i understand it. you have two momentum vectors to begin with and you need to find the resultant vector. so due to momentum conservation, you get
$$\vec p_1 + \vec p_2 = \vec p_f$$
where $$\vec p_i = m_i v_i$$
the speed that you are after is really $$|\vec v_f|$$

5. Oct 31, 2007

klm

so i dont need the components then? or did i find the components of Vf..?

6. Oct 31, 2007

mjsd

do you know how to handle vectors? do u know how to add them?

first resolve everything into component forms and get two equations: one for each x and y

7. Oct 31, 2007

klm

okay for the first ball: Vx= 2 and Vy= 0
second ball: Vx= -1cos(30)
Vy= -1sin(30)

would the be correct?

8. Oct 31, 2007

HallsofIvy

Staff Emeritus
Let me see if I can give more detail about what you have done.
You have one ball of 20 g (0.02 kg) moving east at 2 m/s. It's scalar momentum is 0.02(2)= 0.04 kgm/s so the vector momentum is $0.04\vec{i}$. I can see no reason to divide by total mass.

You have one ball of 30 g (0.03 kg) moving south at 1 m/s. Its scalar momentum is 0.03(1)= 0.03 kgm/s so the vector momentum is $-0.03\vec{j}$.

The total momentum vector before collision is $0.04\vec{i}- 0.03\vec{j}$.

The combined balls must have the same momentum vector, so letting $\vec{v}$ be its velocity vector, $(0.02+ 0.03)\vec{v}= 0.04\vec{i}- 0.03\vec{j}$.

NOW you can get the velocity vector by dividing that equation by the total mass 0.05 kg: $\vec{v}= 0.80\vec{i}- 0.06\vec{j}$

The speed is the length of that vector.

9. Oct 31, 2007

klm

okay i think i understand what you did...but i thought for some reason you should divide by the total mass, but i think we somehow got to same place either way. but one question, should that 0.06 be 0.6 ( just want to make sure, not trying to be picky :)! so the speed would just be .8^2 + .6^2 and then the square root of that number.

10. Oct 31, 2007

klm

because i seem to be getting 1 and that is incorrect...

11. Oct 31, 2007

saket

That looks good to me! (Assuming +x to be along east direction and +y along north.)
Go ahead...

12. Oct 31, 2007

klm

ok so for ball 2 Vx= -.866 and Vy= .5 and then the magnitude of that is .999
and ball 1 the magnitude is just 2

13. Oct 31, 2007

klm

so if i have to do m1v1+ m2v2 :
(.02)(2) + (.03)(1)

14. Oct 31, 2007

saket

no... u have to conserve linear momentum in each direction seperately! (remember, momentum is a vector quantity.. so treat it as a vector... in 1-D, since it can be only positive or negative direction, you used to get result even considering as scalar -- but with apprpriate positive and negative signs.)

15. Oct 31, 2007

saket

Of course it would be 2 for 1st ball, and 1 for 2nd ball. From this only you got these components!
Maybe it's a typing mistake.. but vy = -.5. Check it.

16. Oct 31, 2007

klm

oh so is it -1
so .04i - .03j

17. Oct 31, 2007

klm

haha yeah sorry. it is -.5, i forgot the neg sign sorry!

18. Oct 31, 2007

saket

Conservation of linear momentum
In x-direction: m1*v1,x + m2*v2,x = (m1 + m2)*vf,x
In y-direction: m1*v1,y + m2*v2,y = (m1 + m2)*vf,y

19. Oct 31, 2007

klm

okay sorry this might be a dumb question, but why do we need to break up the conservation into components?

20. Oct 31, 2007

klm

okay so i got .2804 for vfx and -.3 for vfy and then i just do square them both and take the square root and get .411 which should be the speed correct?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?