a) Write a paragraph describing the particle model. What is it, and why is it important?
b) Give two examples of situations, different from those described in the text, for which the particle model is appropriate.
c) Give an example of a situation, different from those described in the text, for which it would be inappropriate.
Solution:
Part A
The basic idea of the particle model is that we will treat an object as if all its mass is concentrated into a single point. The size and shape of the object will not be considered. This is a reasonable approximation of reality if (i) the distance traveled by the object is large in comparison to the size of the object and (ii) rotations and internal motions are not significant features of the object’s motion. The particle model is important in that it allows us to simplify a problem. Complete reality—which would have to include the motion of every single atom in the object—is too complicated to analyze. By treating an object as a particle, we can focus on the most important aspects of its motion while neglecting minor and unobservable details.
Part B
The particle model is valid for understanding the motion of a satellite or a car traveling a large distance.
Part C
The particle model is not valid for understanding how a car engine operates, how a person walks, how a bird flies, or how water flows through a pipe.