To determine The angle between the positon vector and velocity vector and then angle between the position vector and acceleration vector of the given particle. Explanation Write the position vector using the given coordinates. r = 30 cos 2 t i + 40 sin 2 t j + ( 20 t + 3 t 2 ) k (I). Differentiate the equation (I) with respect to time “ t ”. v = d d t ( r ) v = d d t ( 30 cos 2 t i + 40 sin 2 t j + ( 20 t + 3 t 2 ) k ) = [ ( − 30 sin 2 t ) × 2 ] i + [ ( 40 cos 2 t ) × 2 ] j + [ 20 + 6 t ] k = − 60 sin 2 t i + 80 cos 2 t j + ( 20 + 6 t ) k (II). Again differentiate the equation (II) with respect to time “ t ”. a = d v d t = d ( − 60 sin 2 t i + 80 cos 2 t j + ( 20 + 6 t ) k ) d t = − 120 cos 2 t i − 160 sin 2 t j + 6 k (III). Write the relation between the position vector and velocity vector of the particle. v ⋅ r = v r cos θ 1 (IV). Here, e magnitude of the velocity is v , magnitude of the position vector is r , and the angle is θ . Write the relation between the position vector and acceleration vector of the particle. a ⋅ r = a r cos θ 1 (V). Here, e magnitude of the acceleration is a , magnitude of the position vector is r , and the angle is θ . Conclusion: Substitute 2 s for " t " in equation (I). r = 30 cos ( 2 × 2 ) i + 40 sin ( 2 × 2 ) j + ( 20 × 2 + 3 × 2 2 ) k = − 19.609 i − 30.27 j + 52 k (VI). Calculate the magnitude of position vector. r = ( − 19.609 ) 2 + ( − 30.27 ) 2 + ( 52 ) 2 = 63.28 mm Substitute 2 s for " t " in equation (II). v = − 60 sin ( 2 × 2 ) i + 80 cos ( 2 × 2 ) j + ( 20 + 6 × 2 ) k = 45.41 + − 52.29 j + 32 k \ (VII). Calculate the magnitude of velocity vector

8th Edition

ISBN: 9781119047315

Author: Bolton

Publisher: VST

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 2.7, Problem 165P

To determine

The angle between the positon vector and velocity vector and then angle between the position vector and acceleration vector of the given particle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.6, Problem 164P

Chapter 2.7, Problem 166P

Students have asked these similar questions

Please do not use any AI tools to solve this question. I need a fully manual, step-by-step solution with clear explanations, as if it were done by a human tutor. No AI-generated responses, please.

[Q2]: The cost information supplied by the cost accountant is as follows:Sales 20,00 units, $ 10 per unitCalculate the (a/ newsale guantity and (b) new selling price to earn the sameVariable cost $ 6 per unit, Fixed Cost $ 30,000, Profit $ 50,000profit ifi) Variable cost increases by $ 2 per unitil) Fixed cost increase by $ 10,000Ili) Variable cost increase by $ 1 per unit and fixed cost reduces by $ 10,000

can you please help me perform Visual Inspection and Fractography of the attatched image: Preliminary examination to identify the fracture origin, suspected fatigue striation, and corrosion evidences.

Chapter 2 Solutions

EBK ENGINEERING MECHANICS: DYNAMICS, SI

Ch. 2.2 - Prob. 1P Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Problems 2/1 through 2/8 treat the motion of a...Ch. 2.2 - Prob. 9P Ch. 2.2 - A particle in an experimental apparatus has a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.