Abstract
The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts.
Highlights
We are exposed to a wide variety of external motion and movement on a daily basis
Being exposed to changes in motion and movement can have significant biomechanical effects on the human body and, in general we try to minimise our exposure to movement
As concrete illustrations of the concepts, we present in some detail examples for roller coasters and trampolines, using authentic data
Summary
We are exposed to a wide variety of external motion and movement on a daily basis. From driving a car to catching an elevator, our bodies are repeatedly exposed to external forces acting upon us, leading to acceleration. A passenger in a constantly accelerating car will feel a constant force from the seat on his or her body. The term snap will be used throughout this paper to denote the fourth derivative of displacement with respect to time. (Law II: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.) [2] This wording can be interpreted as the impulse force where the force acts over a period of time Dt. If the force is impulsive it follows that the acceleration cannot be constant (if the mass of the body remains unchanged). What are snap, crackle and pop? Below, we consider numerical examples in connection with a few familiar situations
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