Explanation Given information: r = 8 ( 1 − e − t ) θ = 2 π sin ( π 2 t ) W = 175 l b Formula used: θ = 2 π sin ( π 2 t ) F r = W g ( r ¨ − r θ ˙ 2 ) F θ = F r = W g ( r θ ¨ + 2 r ˙ θ ˙ ) Calculation: As we have given, r = 8 ( 1 − e − t ) ⇒ r ˙ = 8 e − t ; ⇒ r ¨ = − 8 e − t ; We know that, θ = 2 π sin ( π 2 t ) ⇒ θ ˙ = cos ( π 2 t ) ; ⇒ θ ¨ = − π 2 sin ( π 2 t ) ; ⇒ a = a r e r + a θ e θ + a z k ; ⇒ ( r ¨ − r θ ˙ 2 ) e r + ( r θ ¨ + 2 r ˙ θ ˙ ) e θ + a z k ⇒ F = F r e r + F θ e θ + F z k ⇒ m a r e r + m a θ e

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

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

Publisher: McGraw-Hill Education

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Chapter 12.1, Problem 12.67P

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The radial and transverse component of the force at given point.

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Vector Mechanics for Engineers: Dynamics

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The radial and transverse component of the force at given point.

Solution Summary: The author calculates the required radial and transverse component of the force at given point.

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