FHSST Physics/Momentum/Change

= 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

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.