Chapter 2: Space Curves
Section 2.9: Applications to Dynamics
An object of mass 3 kg is traveling counterclockwise around the ellipse 4⁢x2+9⁢y2=36. When it reaches the point 0,−2 its acceleration vector is 3 i+5 j. What is its speed?
The point 0,−2 is on the branch of the ellipse defined by yx= −21−x/32, which has curvature
κ=|y″|1+y′23/2 = 16281−5 x23/2
At x=0, T0=i, N0=j, κ0=162/813/2=2/9, and the equation F=m a becomes
35 = 3(v. 10+29 v2 01)
from which the equation 5=2 v2/3 can be extracted. Since the speed must be positive, v=15/2.
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