# A ball of mass m at rest at the coordinate origin exploded into three equal pieces?

1. Apr 8, 2010

### Student91

A ball of mass m at rest at the coordinate origin exploded into three equal pieces.
At a certain instant, one piece is on the x-axis at x=40cm, and another is at x=20cm, y=-60cm. where is the third piece at that instant

I don't have an idea how to solve it I tried many time but I don't reach an answer.

I have to use Fex=Mac.m

2. Apr 8, 2010

### Stonebridge

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

It is solved using conservation of momentum; or centre of mass considerations. (It amounts to the same thing)
As there are no external forces acting, the centre of mass of the combined 3 fragments cannot have changed position, and must still be at the centre of the coordinate system.
Alternatively, if you let the time interval = t, you can write down the x and y coordinates of the momentum of the 2 known fragments. (You have the distance travelled in that time from the coordinates. Velocity = distance/time)
The total momentum of those two plus the unknown fragment must equal zero.

I don't see how you can use F=ma here.

3. Apr 8, 2010

### Student91

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

My Physics teacher told me it solved by F=ma ..

4. Apr 8, 2010

### Staff: Mentor

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

Sorry to hear that.

Momentum conservation it is.

5. Apr 8, 2010

### Student91

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

Is the answer going to be -60i+60j ?

6. Apr 8, 2010

### Stonebridge

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

What do i and j represent here? Are they unit cm vectors in the x and y directions?
You would normally give the answer as x=-60cm and y=+60cm
How have you calculated those values. You would need to show some working, not a guess.

7. Apr 8, 2010

### Student91

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

My Work :

By Conservation of Momentum :

Pi = Pf
0= mv1 + mv2 + mv3

Devid By 3m ..

= v1 + v2 + v3
= d1/3t + d2/3t + d3/3t

Devide By 3t ..

d3 = -( d1 + d2 )

d3 = -( 40i + 20i - 60j )

d3 = -40i - 20i + 60j

d3 = -60i + 60j

So x= -60
and y = 60

8. Apr 9, 2010

### Student91

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

Up !

9. Apr 9, 2010

### Stonebridge

Re: A ball of mass m at rest at the coordinate origin exploded into three equal piece

Yes those answers are correct. (In centimeters)