Jerk (physics) - Non-calculus Explanation

Non-calculus Explanation

Jerk can be difficult to conceptualize when it is defined in terms of calculus. When a force (push or pull) is applied to an object, that object starts to move. As long as the force is applied, the object will continue to speed up. When described in these terms, we are oversimplifying slightly. We think along the lines that there is no force on the object, then all of the sudden there is a force on the object. We do not think about how long it takes to apply the force.

However, in truth, the application of force does not instantly happen. A change always happens over time. Jerk is the change in acceleration over time. Typically, the time of contact where a force is applied is a split second.

If you push on a wall, it takes a fraction of a second before you apply the full push. Your fingertips will squoosh slightly as you begin to push. How long the squooshing takes determines the jerk. If you push on a wall very slowly, you can actually feel your push increasing. In such a case, the jerk is very low, because the change in force is happening over a relatively long time of several seconds. Jerk happens when a force is applied and removed. But the whole time a force is acting consistently on an object, there is no jerk. (This is because the acceleration is constant when there is a constant force.)

How quickly the force starts its push or pull determines the yank and subsequently the jerk. In most applications, it is not important how quickly the force is applied, and thus we typically think of forces being applied instantaneously. In this way, jerk can seem counter-intuitive, because it is not something people experience qualitatively on a daily basis.

If you take a piece of paper in your hands, holding it on both ends, you can pull very hard and not tear the paper. But if you put your hands close together and then jerk on the paper, you can tear it. You do not even have to pull hard. That's because you are using a high jerk (high acceleration in short time) to tear the paper. The paper's fibers require a small amount of time to respond to your pull and pull back. (In rheology, this is called the relaxation time.) If you pull too fast, the paper simply snaps in half. You can similarly jerk on silly putty and snap it in half. The speed at which you pull, and not how hard, determines whether the silly putty snaps or stretches. To be clear, the key is how long it takes to go from zero acceleration to the full application of acceleration. This is not the same thing as how long you pull on the paper, but rather how long the snapping of the paper side to side lasts.