FACULTY OF SCIENCE, AUTUMN 2007

PHYS 124 LEC A1 : Particles and Waves (Instructor: Marc de Montigny)

Walker, Physics, Chapter 5: Newton's Laws of Motion

• Section 5-1: Force and Mass
  • You may read this short section on p. 108.
  • Force is a vector (unit: N = kg m/s²). Mass is a scalar (unit: kg).
  • Mass is a measure of the inertia of a given object. Inertia, in turn, is the tendency of an object to oppose any change of velocity.
  • Various types of forces are discussed in this chapter. Many examples will be discussed in Chapter 6.
• Section 5-2: Newton's First Law of Motion
  • You may skim through pp. 108-110.
  • "No net force" does not mean that there are no forces; it means that the sum of all forces present is equal to zero.
  • Note that this law (as well as Newton's Second Law) is valid in non-accelerated frames of reference only. The use of accelerated frames of reference generally implies the introduction of so-called fictitious forces (e.g. centripetal force, accelerating or deccelerating bus), which are needed by the accelerated observer to account for apparent forces caused by the acceleration.
• Section 5-3: Newton's Second Law of Motion
  • Newton's Second Law is given by Eq. 5-1 on p. 111.
  • Of practical interest is the Section Free-Body Diagram, P. 113, Figure 5-5.
  • P. 117, Example 5-2, discussed in class.
  • P. 140, Problem 57, solved in class
  • Although we do not discuss more examples as this point, we will use the Second Law time and again in the next Chapter.
• Section 5-4: Newton's Third Law of Motion
  • Notation: F_AB denotes the force exerted upon object A by force B
  • Using this notation, Newton's Third Law (see P. 118) reads
    F_BA = - F_AB
    
  • Brief discussion of p. 120, Example 5-4(a) and Example 5-4(b).
  • Here is a riddle for you:
    Consider a horse attempting to pull a wagon from rest on a rough surface. A student who misunderstood Newton's Third Law makes the following statement: "If the horse pulls forward on the wagon, then Newton's law of action-reaction holds that the wagon pulls back equally hard on the horse. Thus, the forces cancel and the system cannot be set in motion."
    Explain briefly what is incorrect with the statement of this student.[from my Spring 2006 Mid-Term]
    Answer
    
• Section 5-5: The Vector Nature of Forces: Forces in Two Dimensions
  • Eq. 5-1 of p. 111 reads explicitly as follows:
    ∑ F_x = ma_x, ∑ F_y = ma_y
    Should we work in three dimensions, we would need to add a third equation : ∑ F_z = ma_z.
  • P. 138, Problem 28, solved in class.
• Section 5-6: Weight
  • P. 124, Eq. 5-5: W = mg
  • Weight is not the same as mass: weight is a force.
  • Denoted by W.
  • Section Apparent Weight on pp. 126-128 omitted temporarily. We will return to it after Section 5-7.
• Section 5-7: Normal Forces
  • Hereafter, normal means "perpendicular".
  • Denoted by N.
  • Warning: as mentioned in paragraph 3 of Section 5-7, in general, the normal force may or may not be equal in magnitude to the weight of an object. This is illustrated by p. 129, Figure 5-13.
  • We will discuss the components of the weight of an object on an inclined surface, p. 131, Figure 5-15.
  • In problems where one requires an object to leave some surface, the point is to set the normal force equal to zero. In other words, "to leave the surface", or "not to touch", means N = 0.
  • When objects are piled up on top of another, it is convenient to use again the notation N_AB to represent the "normal force exerted upon surface A by surface B".
  • Back to Section Apparent Weight, pp. 126-128. In short, the "apparent weight" of an object is simply the normal force acting by the floor (or scale, etc.) on this object. See p. 126, Figure 5-11. The apparent weight often involves the acceleration. For instance, you feel heavier in an elevator that accelerates upward, because the floor exerts upon you a normal force greater than your bodyweight.
  • P. 127, Example 5-7, will be discussed in class.

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