Question

A giant "egg" explodes as part of a fireworks display. The egg is at rest before the explosion, and after the explosion, it breaks into two pieces, with piece B moving in the positive x direction. The masses of both pieces are indicated in (Figure 1) , shown traveling in opposite directions.

The component of the momentum of piece B, pBx,f, is measured to be +500 kg?m/s after the explosion. Find the component of the momentum pAx,f of piece A after the explosion.

Answer 1

Concepts and reason

The main concept used to solve the problem is law of conservation of momentum.

Use law of conservation of momentum to calculate the momentum of the piece A after the explosion.

Fundamentals

The conservation of momentum states that the initial momentum is equal to the final momentum. It is expressed as follows:

${\vec p_{\rm{e}}} = {\vec p_{{\rm{Af}}}} + {\vec p_{{\rm{Bf}}}}$

Here, ${\vec p_{\rm{e}}}$ is the momentum of the giant egg before explosion, ${\vec p_{{\rm{Af}}}}$ is the final momentum of piece A and ${\vec p_{{\rm{Bf}}}}$ is the final momentum of piece B.

According to the law of conservation of momentum,

${\vec p_{\rm{e}}} = {\vec p_{{\rm{Af}}}} + {\vec p_{{\rm{Bf}}}}$

The egg is at rest before the explosion, so the momentum must be zero.

Substitute $0{\rm{ kg}} \cdot {\rm{m/s}}$ for ${\vec p_{\rm{e}}}$ in above equation as follows:

$\begin{array}{c}\\0{\rm{ kg}} \cdot {\rm{m/s}} = {{\vec p}_{{\rm{Af}}}} + {{\vec p}_{{\rm{Bf}}}}\\\\{{\vec p}_{{\rm{Af}}}} = - {{\vec p}_{{\rm{Bf}}}}\\\end{array}$

The piece B is moving along positive x- direction. Hence, the momentum of the piece B is given by,

${\vec p_{{\rm{Bf}}}} = 500{\rm{ kg}} \cdot {\rm{m/s}}\left( {\hat x} \right)$

Substitute $500{\rm{ kg}} \cdot {\rm{m/s}}\left( {\hat x} \right)$ for ${\vec p_{{\rm{Bf}}}}$ in equation ${\vec p_{{\rm{Af}}}} = - {\vec p_{{\rm{Bf}}}}$ for ${\vec p_{{\rm{Bf}}}}$ in above equation as follows:

$\begin{array}{c}\\{{\vec p}_{{\rm{Af}}}} = - 500{\rm{ kg}} \cdot {\rm{m/s}}\left( {\hat x} \right)\\\\ = 500{\rm{ kg}} \cdot {\rm{m/s}}\left( { - \hat x} \right)\\\end{array}$

Therefore, the x component of the momentum of the piece A after the collision is ${p_{{\rm{Ax,f}}}} = - 500{\rm{ kg}} \cdot {\rm{m/s}}$.

Ans:

The component of the momentum ${p_{{\rm{A,f}}}}$ of piece A after the explosion is $- 500\,{\rm{kg}} \cdot {\rm{m/s}}$.