Chapter 2: Space Curves
Section 2.9: Applications to Dynamics
A coin weighing d pounds remains on a disk turning at a uniform speed of 45 rpm if the force on it is not more than d/9 pounds. How far (in inches) from the center of the disk can this coin sit without sliding off?
Table 2.9.5(a) lists the information given in the statement of the example. The unknown distance from the center of the disk is r.
weight: w=d pounds
mass: m=d/g slugs
angular velocity: ω=45 rpm = 452 π radians/min = 9060π=3 π/2 radians/s
linear velocity (speed): v=ω r=3 π r/2 ft/s
Maximum value of FN=m κ v2: d/9 lbs.
Table 2.9.5(a) Given information
From the inequality FN = m κ v2≤d/9 lbs, obtain d/g κ v2≤d/9, or, by making the appropriate substitutions from Table 2.9.5(a),
d/32 1/r 3 π r/22≤d/9
Consequently, r≤12881 π2=0.1601124877 ft, or 12881 π2⋅12=1.921349852 inches.
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