Let’s take a look at the impulse momentum theorem in action.  We saw in the last lesson that the equation for the impulse-momentum theorem is

\(\color{black}{ \Sigma \vec{F} \Delta t = \Delta m \vec{v}.}\)

For a fixed momentum change, we can vary the net force and the time.  In the following examples, we assume that an object of a given mass has a fixed change in speed.  This results in a fixed change in momentum on the right hand side of the impulse-momentum theorem’s equation.

The Impulse Momentum Theorem in Action

Boxing Gloves

For example, boxers use boxing gloves.  The padding in the gloves increases the time it takes the fist inside to stop.  Assume that the boxer throws consistent punches with the same speed.  The gloved hand takes longer to stop, resulting in a lower force.  If they threw the same punch without the glove, the shorter stopping time would result in an increased force.  This would result in more damage to the face being punched and to the fist throwing the punch.

In other types of contact sports, you can see the impulse-momentum theorem in action when someone rolls with a punch.  The increased contact time when you roll decreases the net force of the punch.  Fighters are often knocked out when they move into a punch, decreasing the time of interaction, resulting in a larger force.

Air Bags

The air bag in your car is designed to inflate quickly when the car runs into something.  Suppose you run off the road and into a tree.  The air bag quickly inflates.  Because of your inertia, you continue to move forward into the now inflated air bag.  You come to a rest in a longer time than you would have if you had impacted the steering wheel, dashboard or windshield.

The impact time with the air bag is still relatively short, but longer than the impact time with the dashboard.  If the impact time is twice as long with the air bag, the resulting force is only half the force you would have had with the dashboard.

Deployed Air Bag

Air bags increase the time it takes you to stop, decreasing the net force on you.
Photo by Adam Bartlett, flickr.com
Creative Commons license.