FHSST Physics/Momentum/Change

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Momentum
Definition - Momentum of a System - Change in Momentum - Properties - Impulse - Important Quantities, Equations, and Concepts

Change in Momentum[edit]

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[edit]

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.