Chapter 2: Space Curves
Section 2.9: Applications to Dynamics
What is the maximum magnitude of the force needed to cause an object weighing 2 pounds to move at the constant speed of 3 ft per second along the parabola y=x2?
Table 2.9.5(a) lists the information given in the statement of the example.
weight: w=2 lbs.
mass: m=w/g=2/32=1/16 slugs
speed: v=3 ft/s
curvature: κ=y″1+y′23/2=2/1+4 x23/2
Table 2.7.6(a) Given information
Since v is constant, v.=0, so a=v. T+κ v2 N reduces to a=κ v2 N. Hence,
F=m a=m κ v2 = 1/16 21+4 x23/2 32 = 981+4 x23/2
is to be maximized. By inspection, the maximum of 9/8 occurs at x=0.
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