Chapter 2: Space Curves
Section 2.9: Applications to Dynamics
At a point on a plane curve Rx the curvature is κ=2, T=i, N=−j, and the force on an object weighing 8 pounds is F=i−2 j pounds. Calculate v and v. at this point.
Since a weight of 8 lbs has a mass of 8/32 =1/4 slug, Newton's second law F=m a=m R.. gives
R..=F/m = 41−2=4−8
Now v.=R..·T = 4−8·10 = 4 and κ v2=R..·N = 4−8·0−1=8, so v2=4 and v=2. (The speed v is the norm of R., so is necessarily positive.)
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