FACULTY OF SCIENCE, AUTUMN 2007

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

Walker, Physics, Chapter 6: Applications of Newton's Laws

• Section 6-1: Frictional Forces
  • Kinetic Friction: f_k
    • Kinetic relates to surfaces in relative motion. (From the Greek word kinein, "to move".)
    • P. 143, Eq. 6-1 (f_k = μ_k N), is utilized when the two surfaces slide against one another. It states that the magnitude of the force is proportional to the magnitude of the normal force.
    • Bottom of p. 143: Rules of Thumb for Kinetic Friction. (f is proportional to N, and independent of relative speed and area of surfaces.)
    • P. 145, Example 6-2
    • Example: p. 171, Prob. 14
  • Static Friction: f_s
    • "Static" means "at rest"; it pertains to surfaces which do not slide against one another.
    • Unlike the kinetic friction, there is no general equation which gives the force of static friction. Much like the normal force, it simply balances other forces in Newton's Second Law, from which it is obtained.
    • Eq. 6-2, p. 147, means that f_s can hold an object, up to a maximum value, f_s,max, given by Eq. 6-3.
    • Table 6-1
• Once again, note the difference between f_k and f_s: Eq. 6-1 is an equality which gives f_k, whereas Eq. 6-3, although similar, does not give f_s, but its maximum possible value.
• Question: Why are there no arrows above f_k, f_s and N in Eqs. 6-1 and 6-3?
• Questions: Suppose a block rests on a horizontal plane, and then one starts inclining the plane, i.e. with increasing angle.
  • (a) Before the block starts sliding along the surface, is the force of friction static or kinetic?
  • (b) Just when it starts sliding down the surface, how do you find the force of friction?
  • (c) Once the block is moving down the plane, is the force of friction static or kinetic? How do you calculate it?
• P. 178, Prob. 91, will be solved in class.

Section 6-2: Strings and Springs

• Strings and Tensions:
  • The tension in a string is the force with which each point of the string is held against neighboring points, as illustrated on p. 150, Fig. 6-5.
  • Tension is denoted T
  • As explained in the penultimate paragraph of p. 150, we will consider ropes, strings, wires that are massless, unless stated otherwise, so that the tension is the same throughout their length. (For massive strings, the weight of the string segments contribute to changing the tension.)
  • An "ideal pulley" has no mass, no friction in its bearings, and it simply changes the direction of the tension in a string, without changing its magnitude.
  • P. 176, Prob. 67 to be solved in class.
• Springs, Hooke's Law:
  • Hooke's Law given in Eqs. 6-4, 6-5 of p. 153: F_x = - k x.
  • The constant k may be referred to as force constant, spring constant, or Hooke's constant. Units: N/m.
  • The negative sign in Eq. 6-4 means that F and x have opposite directions, as shown in Fig. 6-8.
  • Henceforth we will be considering "ideal springs", that are massless and assumed to obey Hooke's Law exactly.
  • P. 176, Prob. 66 to be discussed in class.

Section 6-3: Translational Equilibrium

• No new forces here. Just the definition of translational equilibrium, p. 154, Eq. 6-6. Equilibrium implies that velocity does not change. Therefore, acceleration is zero.
• Take a look at Example 6-5, p. 156, as well as Active Example 6-3, p. 157.

Section 6-4: Connected Objects

• This section contains applications of the theory covered in previous sections.
• Example: p. 174, Prob. 37, solved in class.
• P. 161, Example 6-7 Atwood's Machine. Briefly discussed, and to be considered in lab.

Section 6-5: Circular Motion

• Remember that when an object moves along a circular trajectory with speed v (constant or not), it accelerates toward the centre of rotation, because the direction of the velocity vector changes, whether the speed is constant or not.
• P. 163, Eq. 6-15 : a_cp = v²/r
• I find Eq. 6-16 (f_cp = m a_cp) confusing for nothing. The "centripetal force" is not really a new type of force. It is nothing but a fancy name for what should simply be called, "the net force exerted on an object so that gives it a circular motion".
  In practice, you will simply add up the forces, without bothering with centripetal force. The net force then is simply equal to ma_cp. What really deserves to be called "centripetal" is the acceleration, not the force.
• P. 162, Figure 6-13 shows the change of velocity.
• P. 162, Figure 6-12: Swinging a ball
• Remember: When an object moves along a circle, it has a centripetal acceleration.
• P. 174, Prob. 50, solved in class
• P. 165, Example 6-9, Banked Curves (and modified version) discussed in class.

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