Explanation Given: The angular velocity of link A B is ω A B = 5 rad/s . The angular velocity, angle and position vector for point B C are shown in Figure (1). Refer Figure (1): Write the expression for velocity of C relative to B in Cartesian vector form. v C = v B + ω B C × r C / B (I). Write the expression for absolute velocity v B at point B in Cartesian vector from. v B = ω A B × r B / A (II). Write the angular velocity ω A B in Cartesian vector form. ω A B = − ω A B k (III). Write the expression for position vector r B / A form A to B . r B / A = ( − 0.05 cos 45 ° i − 0.05 sin 45 ° j ) m Write the expression for absolute velocity v C in Cartesian vector from. v C = ( − υ C i ) m/s Write the angular velocity ω B C in Cartesian vector form. ω B C = ω B C k (IV). Write the expression for position vector r C / B form C to B . r C / B = ( − 0.2 cos 45 ° i + 0.2 sin 45 ° j ) m The angular velocity, angle and position vector for point E D are shown in Figure (2). Refer Figure (1) and write the expression for velocity of P relative to C in Cartesian vector form. v P = v C + ω B C × r P / C (V). Refer Figure (2) Write the expression for velocity of D relative to P in Cartesian vector form. v D = v P + ω D E × r D / P (VI). Write the expression for absolute velocity v D at point D in Cartesian vector from. v D = υ D i Write the expression for absolute velocity v C at point C in Cartesian vector from. v C = − υ C i (VII). Write the angular velocity ω B C in Cartesian vector form. ω B C = ω B C k (VIII). Write the expression for position vector r P / C form P to C . r P / C = ( − 0.02 i ) m Write the angular velocity ω D E in Cartesian vector form. ω D E = ω D E k Write the expression for position vector r D / P form D to P . r D / P = ( − 0.02 i ) m Write the expression for absolute velocity v D at point D in Cartesian vector from. v D = − υ D i (IX). Write the expression for absolute velocity v E at point E in Cartesian vector from. v E = { ( υ E ) x i + ( υ E ) y j } m/s Write the angular velocity ω D E in Cartesian vector form. ω D E = − ω D E k (X). Write the expression for position vector r E / D form E to D . r E / D = [ ( − 0.05 ) cos 45 ° i + ( 0.05 ) sin 45 ° j ] m Write the expression for velocity of E relative to D in Cartesian vector form. v E = v D + ω D E × r E / D (XI). Write the expression for the magnitude of relative velocity υ E . υ E = ( υ E ) x 2 + ( υ E ) y 2 (XII). Here, the magnitude of relative velocity is υ B / A and the velocity components is υ x and υ y . Calculate the direction of velocity υ E . tan θ = ( υ E ) y ( υ E ) x (XIII). Conclusion: Substitute 5 rad/s for ω A B in Equation (III). ω A B = − 5 k Substitute ( − 0.05 cos 45 ° i − 0.05 sin 45 ° j ) m for r B / A and − 5 k for ω A B in Equation (II). v B = ω A B × r B / A = [ − 5 k × ( − 0.05 cos 45 ° i − 0.05 sin 45 ° j ) ] Substitute ω B C k for ω B C , ( − υ C i ) m/s for v C , [ − 5 k × ( − 0.05 cos 45 ° i − 0.05 sin 45 ° j ) ] for v B and ( − 0.2 cos 45 ° i + 0.2 sin 45 ° j ) m for r C / A in Equation (I). v C = v B + ω B C × r C / B ( − υ C i ) = [ − 5 k × ( − 0.05 cos 45 ° i − 0.05 sin 45 ° j ) + ω B C k × ( − 0.2 cos 45 ° i + 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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 16.5, Problem 80P

To determine

The velocity of point E .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.5, Problem 79P

Chapter 16.6, Problem 2PP

Students have asked these similar questions

(Three-Dimensional Motion) The figure below represents a pair of bevel gears A and B. Gear A rotates in ahorizontal plane about a vertical axis at O. Gear B rotates around the shaft OC,which in turn rotates about the terminal axis at O. At the instant shown, theangular velocity of the shaft OC is 10j rad/sec, and gear A is stationary. Deter-mine the angular velocity of gear B, and the velocity of a point D at the top ofgear B.

The figure below represents a pair of bevel gears A and B. Gear A rotates in ahorizontal plane about a vertical axis at O. Gear B rotates around the shaft OC,which in turn rotates about the terminal axis at O. At the instant shown, theangular velocity of the shaft OC is 10j rad/sec. If gear A has an angular velocityof 4j rad/sec, determine the angular velocity of gear B.

Solve using relative motion analysis velocity

Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1P Ch. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P

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.

The velocity of point E .

Solution Summary: The angular velocity, angle and position vector for point BC are shown in Figure (1).

Concept explainers

Videos

The velocity of point E .

Want to see the full answer?

Chapter 16 Solutions