20141002

Physics presentation: impulse and momentum

Whuuuuuuut. (Video link: "bowling strike with a ping pong ball.")

In this presentation we will introduce another new connection between forces and motion, in terms of how the net force can exert an impulse on an object in order to change its momentum. This is yet another new approach to connecting forces and motion, compared to the previous discussion in this course of using Newton's laws to relate how forces on an object result in a net force that may or many not change its motion, and analyzing how forces can do work on or against an object in order to speed up or slow down its motion.

First, defining the momentum of an object, and then expressing how the net force can exert an impulse on this object.

The first slide showing a ping-pong ball knocking over all ten bowling pins should seem very strange to you, as the mass of the ping-pong ball is too small to effectively bowl a strike, even if it were traveling with a supersonic speed. In order to fully account for the "knocking-over" strength of a moving object, then, we must include mass as well as its speed (and direction) to define its momentum p.

Momentum p is a vector quantity (so don't forget to draw an arrow over it) whose magnitude depends both on the mass and speed of the object, with the combined units of both mass and speed (kg·m/s).

We also need to introduce the concept of impulse J, which is the product of the net force acting on an object and the duration of time that the net force acted on this object (whether for a brief instant, or for a prolonged period). (Video link: "Teaching Tee Ball Hitting.")

Impulse has the combined units of both force and time (N·s). Here we use the somewhat obscure (but totally legit) "J" symbol for impulse, remembering to draw an arrow over it (as it is a vector quantity). (It turns out that "I" is already reserved for rotational inertia in the next section.)

Second, let's now explicitly make the connection between the impulse acting on an object, and the resulting change in the momentum of the object.

This is an incomplete form of the total momentum conservation equation we will utilize later, but this "impulse-momentum theorem" shows how the impulse (exerted by the net force acting over a specific duration of time) causes a corresponding initial-to-final change in the momentum of the object.

Let's apply these concepts to understand why you should be driving in a car with air bags and with your seat belts on. (Video link: "Crash test with and without safety belt.")

The crash-test dummy in either car has the same mass and initial velocity. Once each has come to a complete stop (whether by slamming into the car dashboard, or being restrained by the airbag and seatbelt), which crash-test dummy (in the car with no seatbelt nor airbag, or in the car with a seatbelt and airbag) would have:
...a greater magnitude momentum change ∆p?
...a greater magnitude impulse J exerted on it?
...a longer stopping time ∆t? (Note that both cars have the same stopping time, but each crash-test dummy takes a different amount of time to first come to a stop by slamming into whatever is in front of it.)
...a greater magnitude net (stopping) force ΣF exerted on it?
Then as a result, which crash-test dummy (in the car with no seatbelt nor airbag, or in the car with a seatbelt and airbag) would have less serious injuries?

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