Explanation Given: The particle traveling in an elliptical spiral path is shown in Figure (1). The equation of position vector is r = { ( 2 cos ( 0.1 ) t ) i + ( 1.5 sin ( 0.1 ) t ) j + ( 2 t ) k } m . The time is 8 s . Write the expression of position of the particle in vector form. r = { ( 2 cos ( 0.1 ) t ) i + ( 1.5 sin ( 0.1 ) t ) j + ( 2 t ) k } m (I). Write the expression to calculate the velocity ( v ) . v = d r d t (II). Here, the velocity in vector form is v and rate of change of position of the particle with respect to time is d r d t . Write the expression to calculate the acceleration ( a ) . a = d v d t (III). Here, the acceleration in vector form is a and rate of change of velocity with respect to time is d v d t . Conclusion: Substitute { ( 2 cos ( 0.1 ) t ) i + ( 1.5 sin ( 0.1 ) t ) j + ( 2 t ) k } m for r in Equation (II). v P = d d t { ( 2 cos ( 0.1 ) t ) i + ( 1.5 sin ( 0.1 ) t ) j + ( 2 t ) k } m = − 0.2 sin ( 0.1 t ) i + 0.15 cos ( 0.1 t ) j +2 k (IV). Substitute 8 s for t in Equation (IV). v P = − 0.2 sin ( 0.1 ( 8 ) ) i + 0.15 cos ( 0.1 ( 8 ) ) j +2 k v P = { − 0.14347 i + 0.10451 j +2 k } m/s (V). Substitute − 0.2 sin ( 0.1 t ) i + 0.15 cos ( 0.1 t ) j +2 k for v in Equation (III). a P = d d t { − 0.2 sin ( 0.1 t ) i + 0.15 cos ( 0.1 t ) j +2 k } = { − 0.02 cos ( 0.1 t ) i − 0.015 sin ( 0.1 t ) j } m/s 2 (V)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.7, Problem 152P

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The coordinate direction angles α,β and γ .

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Chapter 12.7, Problem 151P

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The coordinate direction angles α , β and γ .

Solution Summary: The particle traveling in an elliptical spiral path is shown in Figure (1). Write the expression of position of the particle in vector form.

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The coordinate direction angles α,β and γ .

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