A conical pendulum consists of a ball (mass=3 kg) fixed on the end of a massless cord. The ball moves at a constant velocity of of v=3 m/s in uniform circular motion. The length of the cord is L=5 m. Find the angle a that the cord makes with respect to the the y-axis. g=9.8 m/s^2, r=radius of motion Eq 1: g tan(a)=v^2/r Eq 2: r=L sin(a) Substituting Eq 2 into Eq 1 gives g tan(a)=v^2/L sin(a), which becomes tan(a)sin(a)=v^2/gL or, sin^2(a)/cos(a)=v^2/gL How do I solve for angle a?
A conical pendulum consists of a ball (mass=3 kg) fixed on the end of a massless cord. The ball moves at a constant velocity of of v=3 m/s in uniform circular motion. The length of the cord is L=5 m. Find the angle a that the cord makes with respect to the the y-axis. g=9.8 m/s^2, r=radius of motion Eq 1: g tan(a)=v^2/r Eq 2: r=L sin(a) Substituting Eq 2 into Eq 1 gives g tan(a)=v^2/L sin(a), which becomes tan(a)sin(a)=v^2/gL or, sin^2(a)/cos(a)=v^2/gL How do I solve for angle a?
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 49P
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A conical pendulum consists of a ball (mass=3 kg) fixed on the end of a massless cord. The ball moves at a constant velocity of of v=3 m/s in uniform circular motion. The length of the cord is L=5 m. Find the angle a that the cord makes with respect to the the y-axis. g=9.8 m/s^2, r=radius of motion
Eq 1: g tan(a)=v^2/r
Eq 2: r=L sin(a)
Substituting Eq 2 into Eq 1 gives
g tan(a)=v^2/L sin(a),
which becomes
tan(a)sin(a)=v^2/gL
or, sin^2(a)/cos(a)=v^2/gL
How do I solve for angle a?
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