Problem Solving Guide

Algorithm

Misconceptions & Mistakes

 

This Flipping Physics video provides an explanation that might help clarify a common misconception when applying Newton's 3rd law; Force pair clarification.


 
 
This Veritasium video reveals a huge misconception; Equal and opposite forces.

 
 
Another Doc Schuster video looking at Newton's 3rd law. This video even looks at what happens if you apply a force very quickly; Hints at the notion that all of Newton's laws are independent of one another, (i.e. you can not derive one from the other). This video looks at the 2nd and 3rd law.

Pro Tips

 
  • Remember that force pairs always act on different objects and in opposite directions but with the same magnitude.
  • Take great care in using subscripts to label forces. The subscripts will make identifying force pairs much easier.
  • When looking at the forces always start by identifying the object (that the force is acting on) and the agent (what is applying the force). These two objects will have force pairs on them. For more info on identifying forces see here.

Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways. 

Physical

Physical Representations describes the physical phenomena of the situation in a visual way.

 This image shows two scenarios of an object moving. Each image shows a variety of forces acting on the object denoted as arrows and the kind of force and the direction that it acts on the object. There is also an arrow showing the direction of the net force which also shows the direction of acceleration. Each image shows a free body diagram of all of the forces that is acting on the object to show a physical representation of all of the forces as well as their magnitudes and direction.

Mathematical

Mathematical Representation uses equation(s) to describe and analyze the situation.

The main mathematical representation for forces will be applying Newton's Second Law to a physical problem. You will need to analyze the motion of an object and create a free body diagram of the relative forces in order to derive the force equations. We learned in the kinematics section how to analyze motion without any concern about the forces that caused the motion. The infographic below describes the relationship between force and acceleration. Thus, we may now analyze the forces acting on an object to determine the relative acceleration.

A representation with the words newton's second law (n.two.l) on the top. There is an equation that shows that the sum of all of the forces external to the system, acting on the system, is equal to the mass of the system multiplied by the acceleration of the center of mass of the system. This is also written in words below with the note that says that this equation contains vector and scalar quantities.

 

Graphical

Graphical Representation describes the situation through use of plots and graphs.

A graph of force in newtons on the y axis and time on the x axis with two graphs. The blue graph is a positive curve and the red curve is a negative curve where they both are zero before and after the curve. This is a representation of force pairs and that they are equal and opposite in magnitude

Descriptive

Descriptive Representation describes the physical phenomena with words and annotations.

 A physics student is pushing a $17 \; kg$ crate across a frictionless floor with an acceleration of $0.25 \; m/s^{2}$. What is the relative force the student is applying? We know the mass of the crate, and that the acceleration is a constant $0.25 \; m/s^{2}$. Therefore, we may apply the mathematical representation and determine the relative force the physics student is applying to the crate.

Experimental

Experimental Representation examines a physical phenomena through observations and data measurement.

 We could go out and physically push a $17 \; kg$ crate on a mostly frictionless surface and measure the average distance we travel for some period of time. By measuring the average distanced traveled per unit time, we can determine the acceleration by determining the slope of a velocity versus time graph. This would allow us to use Newton's Second Law and relate the force to acceleration.

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