# FHSST Physics/Momentum/Change

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 ${\displaystyle {\overrightarrow {u}}}$ and a final velocity ${\displaystyle {\overrightarrow {v}}}$, then its change in momentum, ${\displaystyle \Delta {\overrightarrow {p}}}$, is

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

## Worked Example 35 Change in Momentum

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

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 ${\displaystyle 4\ m.s^{-1}}$. The word initial is included here since the ball will obviously slow down with time and ${\displaystyle 4\ m.s^{-1}}$ 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,

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

We have everything we need to find ${\displaystyle \Delta {\overrightarrow {p}}}$. 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

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

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