Explanation Draw the schematic diagram of the system as in Figure (1). Write the expression for the velocity of point A in vector form. v A = v B + v A / B (I) Here, velocity of point A in vector form is v A , velocity of point B in vector form is v B and velocity of point A with respect to point B in vector form is v A / B . Write the expression for the velocity of point A with respect to point B in vector form. v A / B = ω × r A / B (II) Here, angular velocity of the right-angle link in vector form is ω and position vector of point A with respect to point B is r A / B . Conclusion: Write the expression for the angular velocity of the right-angle link in vector form. ω = ω k (III) Here, angular velocity of the right-angle link is ω and unit vector along z -direction is k . Substitute 3 rad / s for ω in Equation (III). ω = ( 3 rad / s ) k = 3 k rad / s Calculate the position vector of point A with respect to point B . r A / B = ( A C ¯ ) i + ( C B ¯ ) j (IV) Here, distance between point A and C is A C ¯ , distance between point C and B is C B ¯ and unit vectors along x and y -direction are i and j respectively. Substitute 0.4 m for A C ¯ and 0.5 m for C B ¯ in Equation (IV). r A / B = ( 0.4 m ) i + ( 0.5 m ) j = 0.4 i + 0.5 j m Substitute 3 k rad / s for ω and 0.4 i + 0.5 j m for r A / B in Equation (II). v A / B = ( 3 k rad / s ) × ( 0.4 i + 0.5 j m ) = − 1.5 i + 1.2 j m / s Substitute 2 i − 0.3 j m / s for v B and − 1.5 i + 1.2 j m / s for v A / B in Equation (I). v A = ( 2 i − 0.3 j m / s ) + ( − 1.5 i + 1.2 j m / s ) = 0.5 i + 0.9 j m / s Hence, the velocity of point A using vector notation is 0.5 i + 0.9 j m / s _ . Write the expression for the magnitude of the velocity of point A with respect to point B . v A / B = ( v A / B ) x 2 + ( v A / B ) y 2 (V) Here, velocity of point A with respect to point B is v A / B and x and y components of velocity of point A with respect to point B are ( v A / B ) x and ( v A / B ) y respectively. Substitute − 1.5 for ( v A / B ) x and 1.2 for ( v A / B ) y in Equation (V). v A / B = ( − 1.5 ) 2 + ( 1.2 ) 2 = 1

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 5.4, Problem 67P

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The velocity of point A using vector notation.

The magnitude of the velocity of point A.

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Chapter 5.4, Problem 66P

Chapter 5.4, Problem 68P

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Engineering Mechanics: Dynamics

Ch. 5.2 - Prob. 1P Ch. 5.2 - The circular sector rotates about a fixed axis...Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - When switched on, the grinding machine accelerates...Ch. 5.2 - The small cart is released from rest in position 1...Ch. 5.2 - The flywheel has a diameter of 600 mm and rotates...Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.2 - The angular acceleration of a body which is...

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The velocity of point A using vector notation. The magnitude of the velocity of point A .

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The velocity of point A using vector notation. The magnitude of the velocity of point A.

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Chapter 5 Solutions

The velocity of point A using vector notation.

The magnitude of the velocity of point A.