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 and a final velocity , then its change in momentum, , 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 . It bounces back with an initial velocity of . 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 . The word initial is included here since the ball will obviously slow down with time and 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,
We have everything we need to find . 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
where we remembered in the last step to include the direction of the change in momentum in words.