# Conservation of linear momentum problem

## Homework Statement

A particle of mass 5m moving with speed v explodes and spilts into two pieces with masses of 2m and 3m. The lighter piece continues to move in the original direction with speed 5v relative to the heavier piece. what is the actual speed of the lighter piece?

## Homework Equations

using law of conservation of linear momentum
initial moment = final moment
mass (m) x Velocity (v) = mass (m) x Velocity (v)

## The Attempt at a Solution

using the formula...

5m (v) = 2m(v) - 3m (5v) ....) i used the minus (-) sign because the heavier piece went a different direction

5mv = 2mv -15mv

20mv = 2mv

10v = v

FIRST CLASS TEST IS TOMORROW!

CWatters
Homework Helper
Gold Member
5m (v) = 2m(v) - 3m (5v)

That's not correct. You appear to be assuming that after the explosion the large bit is moving five times faster than the small bit. That's not what the problem states.

i used the minus (-) sign because the heavier piece went a different direction

I wouldn't recommend that. I would just define

Vi is the initial velocity
Vsmall as the new velocity of the small bit
Vlarge as the new velocity of the large bit

So with that in mind it should be something like

5mVi = 2mVsmall + 3mVlarge

I'll let you figure out the other equation to write.

Sorry for the edits to my reply.

ok soo would i know say

5mVi - 3mVlarge = 2mVsmall

Ok i think im confusing myself but i do get and understand what you were saying....i think the "relative" word in the problem is what confusing me...

what do they mean when they say ".....with a speed 5v relative..."

Pleas Helppp...i really want to understand this

Im still stuck on this question can someone give any insights..? PLEASE...

haruspex
Homework Helper
Gold Member
2020 Award
ok soo would i know say

5mVi - 3mVlarge = 2mVsmall
Yes
Ok i think im confusing myself but i do get and understand what you were saying....i think the "relative" word in the problem is what confusing me...

what do they mean when they say ".....with a speed 5v relative..."
it's how much faster it's moving. Vsmall = Vlarge + 5v.