Explanation Given Information: The three dimensional motion of a particle is defined by the position vector r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k . Calculation: Write three-dimensional motion of particle in term of position vector equation. r = ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k Write the expression for velocity using the relation: v = d r d t Substitute ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k for r . v = d ( R t cos ω n t ) i + c t j + ( R t sin ω n t ) k d t = R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k Write the expression for acceleration using the relation: a = d v d t Substitute R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k for v . a = d ( R ( cos ω n t − ω n sin ω n t ) i + c j + R ( sin ω n t + ω n t cos ω n t ) k ) d t = R ( − ω n sin ω n t − ω n sin ω n t − ω n 2 t cos ω n t ) i + R ( 2 ω n cos ω n t − ω n 2 t sin ω n t ) k = ω n R ( − ( 2 sin ω n t + ω n t cos ω n t ) i + ( 2 cos ω n t − ω n t sin ω n t ) k ) (1) Calculate the velocity ( v ) of the particle. v 2 = v x 2 + v y 2 + v z 2 Substitute R ( cos ω n t − ω n sin ω n t ) for v x , c for v y and R ( sin ω n t + ω n t cos ω n t ) for v z

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.5, Problem 11.151P

To determine

The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

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Chapter 11.5, Problem 11.150P

Chapter 11.5, Problem 11.152P

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 11.1 - A bus travels the 100 miles between A and B at 50...Ch. 11.1 - Two cars A and B race each other down a straight...Ch. 11.1 - A snowboarder starts from rest at the top of a...Ch. 11.1 - Prob. 11.2P Ch. 11.1 - Prob. 11.3P Ch. 11.1 - A loaded railroad car is rolling at a constant...Ch. 11.1 - Prob. 11.5P Ch. 11.1 - Prob. 11.6P Ch. 11.1 - A girl operates a radio-controlled model car in a...Ch. 11.1 - The motion of a particle is defined by the...

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The radius ( ρ ) of curvature of the path described by the particle when time ( t ) is 0 sec.

Solution Summary: The author describes the three-dimensional motion of a particle defined by the position vector r=(rho ).

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The radius (ρ) of curvature of the path described by the particle when time (t) is 0 sec.

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Chapter 11 Solutions