# Collision question.

• May 5th 2011, 01:34 AM
silvercats
Collision question.
10KG ball travels at a speed(velocity) of 5ms and hits a 4KG balls which is travelling at the speed of 2ms and travelling to the same direction and 1st one.what are the velocities of two balls after the collision.

take e=1/2

I did this but never got the answer in the back of the book.here is how i did
it
M1 <<< doesn't mean M multipied by 1.it is just the notation

by using
(M1*U1 + M2*U2) = (M1*V1 + M2*V2) ---->(left drirection)

10*5 + 4*2=10*V1 + 4*v2 =
58=10*V1 + 4*v2 ------ (1)

using e(U1+U2)=V1+V2
1/2*(5-2)=V2-V1
=(3/2)=V2-V1 -------(2)[!--?can somebody tell me why is this 5-2,not 5+2
even they are travelling to the same direction?(book says so,that is why i
substracted them]

(2) equation * 4
and (1)eq-multiplied (2)nd equation gives:

58-6=10*V1+4V2 - 4*V2+4*V1
52=14V1
v1=13

but that is not the answer given on the book.what is the error?

thanks.
• May 5th 2011, 02:50 AM
bugatti79
Quote:

Originally Posted by silvercats
10KG ball travels at a speed(velocity) of 5ms and hits a 4KG balls which is travelling at the speed of 2ms and travelling to the same direction and 1st one.what are the velocities of two balls after the collision.

take e=1/2

I did this but never got the answer in the back of the book.here is how i did
it
M1 <<< doesn't mean M multipied by 1.it is just the notation

by using
(M1*U1 + M2*U2) = (M1*V1 + M2*V2) ---->(left drirection)

10*5 + 4*2=10*V1 + 4*v2 =
58=10*V1 + 4*v2 ------ (1)

using e(U1+U2)=V1+V2

Your error is the restitution equation. It should be

$\displaystyle \displaystyle \frac{v_2 - v_1}{u_1 - u_2}$
• May 5th 2011, 05:10 AM
topsquark
Quote:

Originally Posted by silvercats
using e(U1+U2)=V1+V2
1/2*(5-2)=V2-V1
=(3/2)=V2-V1 -------(2)[!--?can somebody tell me why is this 5-2,not 5+2
even they are travelling to the same direction?(book says so,that is why i
substracted them]

(2) equation * 4
and (1)eq-multiplied (2)nd equation gives:

58-6=10*V1+4V2 - 4*V2+4*V1
52=14V1
v1=13

but that is not the answer given on the book.what is the error?

thanks.

There are two errors, actually. First is the one bugatti79 pointed out. Actually u2 - u1 = 2 - 5 = -3 because both objects are moving in the positive direction before the collision.

I get v1 = 32/7 = 4.571 m/s and v2 = 43/14 = 3.071 m/s.

IMPORTANT: Also note that the unit for mass is kg not KG. Also the unit for speed is m/s not ms.

-Dan
• May 5th 2011, 05:59 AM
silvercats
book's back side says 26/7 ,73/14 O.o :/
• May 5th 2011, 06:25 AM
bugatti79
Quote:

Originally Posted by silvercats
book's back side says 26/7 ,73/14 O.o :/

Which is what i got.

The 2 equations are

58=10V1+4V2 ( You have this)
1.5=-V1+V2 (You didnt have this because of incorrect restitution formula)
Note that u1 =5 and u2=2

make sense?
• May 5th 2011, 08:09 AM
silvercats
yes.but why is that it is v2-v1 and not v1-v2
and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity?
• May 5th 2011, 08:12 AM
silvercats
Quote:

I get v1 = 32/7 = 4.571 m/s and v2 = 43/14 = 3.071 m/s.
Quote:

book's back side says 26/7 ,73/14 O.o :/
has topsquark made a mistake?it looks like it
• May 5th 2011, 09:50 AM
topsquark
Quote:

Originally Posted by silvercats
has topsquark made a mistake?it looks like it

Why trust the book's answers? Or mine for that matter? Plug them into the equations and see for yourself. We have
$\displaystyle 10 \cdot 5 + 4 \cdot 2 = 10v_1 + 4v_2$

$\displaystyle \frac{1}{2} = \frac{v_2 - v_1}{u_1 - u_2} = \frac{v_2 - v_1}{5 - 2}$

I had the COR equation mixed up. Ah well. I now agree with your book.

-Dan
• May 6th 2011, 12:07 AM
silvercats
hehe....good. btw why is that it is v2-v1 and not v1-v2
and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity? asking again.this the biggest problem for me now.can some one explain..?
What is these balls traveled to opposite directions? (i am cool with the momentum question with this,but that other equation which has 'e')
• May 6th 2011, 01:32 AM
bugatti79
Quote:

Originally Posted by silvercats
hehe....good. btw why is that it is v2-v1 and not v1-v2
and it is u1-u2 not u2-u1 if direction is not the problem but relative velocity? asking again.this the biggest problem for me now.can some one explain..?
What is these balls traveled to opposite directions? (i am cool with the momentum question with this,but that other equation which has 'e')

You would need to see the derivation of this equation to see why it is this way. THis equation holds for 1d impact between particles.

As I have already said, once you know the magnitude and direction of the initial velocities you can determine the final velocities. You can assume a direction of the final velocities and if the calculation yields a negative answer, then the particle is acting acting in the opposite direction to what you assumed.