Explanation Given: The magnitude of force for first case, F = 300 N . The magnitude of force for second case, F = 500 N . Conclusion: First case: Express the position vector r in the direction of a . r a = 2 i + 2 j − 1 k Calculate the length of a . r a = ( r x ) 2 + ( r y ) 2 + ( r z ) 2 (I) Here, the coordinate in the x , y and z direction is r x , r y and r z respectively. Substitute 2 m for r x , 2 m for r y and − 1 m for r z in Equation (I). r a = ( 2 ) 2 + ( 2 ) 2 + ( − 1 ) 2 = 9 = 3 m Calculate the vector force F . F = F r a r a (II) Substitute 300 N for F , 2 i + 2 j − 1 k for r a and 3 m for r a in Equation (II). F = [ ( 300 ) 2 i + 2 j − 1 k 3 ] = { 200 i + 200 j − 100 k } N Express the unit vector in the direction of a-a . u a − a = r a − a r a − a = ( − 3 − 0 ) i + ( 4 − 0 ) j + ( 0 − 0 ) k ( − 3 − 0 ) 2 + ( 4 − 0 ) 2 + ( 0 − 0 ) 2 = − 3 i + 4 j 5 = − 3 5 i + 4 5 j Here, the position vector r in the direction of a-a is r a − a and the length between a-a is r a − a . Express the magnitude of the projection of the force F a − a along a - a axes using dot product in first case. F a − a = F ⋅ u a − a (III) Substitute { 200 i + 200 j − 100 k } N for F and − 3 5 i + 4 5 j for u a − a in Equation (III). F a − a = { 200 i + 200 j − 100 k } ⋅ { − 3 5 i + 4 5 j } = [ − 3 5 ( 200 ) ] + [ 4 5 ( 200 ) ] + [ ( − 100 ) ( 0 ) ] Hence, the magnitude of the projection of the force F a − a along a - a axes using dot product in first case is [ − 3 5 ( 200 ) ] + [ 4 5 ( 200 ) ] + [ ( − 100 ) ( 0 ) ] _

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2.9, Problem 9PP

To determine

How the dot product finds the magnitude of the projection of the force F along a-a axes for both the cases.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.9, Problem 8PP

Chapter 2.9, Problem 25FP

Students have asked these similar questions

Using hand drawing both of them

6. Draw the isometric drawing for this problem(15%)

Please draw the section view of the following problems

Chapter 2 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Two forces act on the hook. Determine the...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - The force F = 450 lb acts on the frame. Resolve...Ch. 2.3 - If force F is to have a component along the u axis...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...

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.

How the dot product finds the magnitude of the projection of the force F along a - a axes for both the cases.

Solution Summary: The author explains how the dot product finds the magnitude of the projection of force F along a-a axes for both cases.

Videos

How the dot product finds the magnitude of the projection of the force F along a-a axes for both the cases.

Want to see the full answer?

Chapter 2 Solutions