Back to Two Dimensions

In the preceding analysis we have considered the location of a force only as to its horizontal position. This analysis is simpler and accurate for our needs. There is, however, a need to at least talk about the effect of the vertical positions of the forces.

The neutral stability case is a convenient dividing point between stable and unstable results. It, however, is not really a position that a real system would remain in for very long. The reason for this is that the CG's of the passenger and the car are above (in the two dimensional world) the pivot point. Starting at the neutral stability point the slightest rotation of the system (car and passenger) counterclockwise will have the effect of moving the falling passenger CG farther to the left, away from he pivot point while at the same time moving the car CG also to the left which is closer to the pivot point. This increases the effect of the passenger weight and decreases the opposing effect of the car weight and results in a increasingly rapid rate of rotation.

For these reasons the configuration of Case #2 is very unstable. It should be noted here that a single passenger of reasonable size can turn over even an extremely heavy car.

Stability Case #3

In looking at what we have done so far it normal to assume that a car would have more than one passenger. For this next case we will add two additional passenger, each of 250 pounds and have them sit in the center of the car. This is shown in Figure 6.

Figure 6 – Stability Case #3 – Additional Passengers in Center

The clockwise torques are:

(1000 pounds + 500 pounds)(4 inches) = 6000 inch pounds

And counterclockwise torques are:

(200 pounds)(20 inches) = 4000 inch pounds

From this we see that the car in now very stable again. We could actually have added any amount in the form of passengers or a heavier car and gotten the same results.