Which of these is a statement of the impulse-momentum theorem

Question

asked Oct 11, 2020 61.7k views

2 Answers

Colin Atkinson · Answer 1 · 2020-10-16T02:10:31+0000

Answer:

The average force times the time of interaction equals the change in momentum

Step-by-step explanation:

The impulse-momentum theorem states that impulse (equal to the average force times the time of interaction) is equal to the change in momentum:

$I=F \Delta t = \Delta p$

where

I is the impulse

F is the average force

$\Delta t$ is the time of the interaction

$\Delta p$ is the change in momentum

We can demonstrate this theorem, by re-writing the force as mass (m) times acceleration (a):

$F \Delta t = ma \Delta t$

The acceleration is equal to the change in velocity divided by the time interval:

$ma \Delta t = m (\Delta v)/(\Delta t) \Delta t$

And by simplifying
$\Delta t$ , we get:

$= m \Delta v = \Delta p$

which is equal to the change in momentum.