# FHSST Physics/Momentum/Change

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Momentum The Free High School Science Texts: A Textbook for High School Students Studying Physics. Main Page - << Previous Chapter (Rectilinear Motion) - Next Chapter (Work and Energy) >> Definition - Momentum of a System - Change in Momentum - Properties - Impulse - Important Quantities, Equations, and Concepts

# Change in Momentum

If either an object's mass or velocity changes then its momentum too will change. If an object has an initial velocity $\overrightarrow{u}$ and a final velocity $\overrightarrow{v}$, then its change in momentum, $\Delta \overrightarrow{p}$, is

 $\Delta \overrightarrow{p}$ = $\overrightarrow{p}_{final}-\overrightarrow{p}_{initial}$ $m\overrightarrow{v}-m\overrightarrow{u}$

## Worked Example 35 Change in Momentum

Question: A rubber ball of mass 0.8kg is dropped and strikes the floor at a velocity of $6\ m.s^{-1}$. It bounces back with an initial velocity of $4\ m.s^{-1}$. Calculate the change in momentum of the rubber ball caused by the floor.

Answer:

Step 1 :

Analyse the question to determine what is given. The question explicitly gives

• the ball's mass,
• the ball's initial velocity, and
• the ball's final velocity

all in the correct units.

Do not be confused by the question referring to the ball bouncing back with an initial velocity of $4\ m.s^{-1}$. The word initial is included here since the ball will obviously slow down with time and $4\ m.s^{-1}$ is the speed immediately after bouncing from the floor.

Step 2 :

What is being asked? We are asked to calculate the change in momentum of the ball,

$\begin{matrix}\Delta\overrightarrow{p} &=& m\overrightarrow{v} - m\overrightarrow{u}.\end{matrix}$

We have everything we need to find $\Delta\overrightarrow{p}$. Since the initial momentum is directed downwards and the final momentum is in the upward direction, we can use the algebraic method of subtraction discussed in the vectors chapter.

Step 3 : Firstly, we choose a positive direction. Let us choose down as the positive direction. Then substituting,

Down is the positive direction

$\begin{matrix}\Delta\overrightarrow{p} &=& m\overrightarrow{v} -m\overrightarrow{u}\\&=& (0.8kg)(-4\ m.s^{-1})-(0.8kg)(+6\ m.s^{-1})\\&=& (0.8kg)(-10\ m.s^{-1})\\&=& -8\ kg.m.s^{-1}\\&=& 8\ kg.m.s^{-1}\textbf{\ up}\end{matrix}$

where we remembered in the last step to include the direction of the change in momentum in words.