Explanation Given: The velocity of B , υ B = 7 m / s . The velocity of A , υ A = 8 m / s . The distance between A and B , r B / A = 2 m . The radius of circular path, r = 1 m . The angular acceleration or speed of B , α B = 4 m / s 2 . The angular acceleration or speed of A , α A = 6 m / s 2 . Conclusion: Express the angular velocity of particle A . Ω = υ A r (I) Substitute 8 m / s for υ A and 1 m for r in Equation (I). Ω = 8 1 = 8 rad / s = { − 8 k } rad / s Express the relative velocity of particle B with respect to A by applying relative velocity equation. v B = v A + Ω × r B / A + ( v B / A ) x y z (II) Substitute { 7 i } m / s for v B , { − 8 i } m / s for v A , { − 8 k } rad / s for Ω and { 2 j } m for r B / A in Equation (II). 7 i = − 8 i + ( − 8 k ) × ( 2 j ) + ( v B / A ) x y z 7 i = − 8 i − 16 i + ( v B / A ) x y z ( v B / A ) x y z = { 31 } i m / s Hence, the relative velocity of B with respect to A is { 31 i } m / s . Express the angular acceleration due to the rotation of x , y , z reference. Ω ˙ = α A r (III) Substitute 6 m / s 2 for α A and 1 m for r in Equation (III). Ω ˙ = 6 1 = 6 rad / s 2 = { − 6 k } rad / s 2 Express the normal component acceleration of A . ( a A ) n = ( υ A ) 2 r (IV) Substitute 8 m / s for υ A and 1 m for r in Equation (IV). ( a A ) n = ( 8 ) 2 1 = 64 m / s 2 Write the given differential equation for parabolic path. y = x 2 (V) Differentiate Equation (V) with respect to x to get, y = x 2 d y d x = 2 x = 0 (VI) Perform double differentiation in Equation (VI) to get, d 2 y d x 2 = 2 Express the radius of the parabolic path. ρ = [ 1 + ( d y / d x ) 2 ] 3 / 2 | d 2 y d x 2 | (VII) Substitute 0 for d y d x and 2 for d 2 y d x 2 in Equation (VII). ρ = [ 1 + ( 0 ) 2 ] 3 / 2 | 2 | = 1 2 m = 0

14th Edition

ISBN: 9780133976601

Author: HIBBELER

Publisher: PEARSON CO

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 16.8, Problem 137P

To determine

The relative velocity and relative acceleration of B with respect to A .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.8, Problem 136P

Chapter 16.8, Problem 138P

Students have asked these similar questions

CORRECT AND DETAILED SOLUTION WITH FBD ONLY. I WILL UPVOTE 4 : A cable and pulley system at D is used to bring a 230-kg pole (ACB) to a vertical position as shown. The cable has tensile force T and is attached at C. The length of the pole is 6.0 m, the outer diameter is d = 140 mm, and the wall thickness t = 12 mm. The pole pivots about a pin at A. The allowable shear stress in the pin is 60 MPa and the allowable bearing stress is 90 MPa. The diameter of the cable is 8 mm.1.Find the minimum diameter (mm) of the pin at A to support the weight of the pole in the position shown.2.Calculate the elongation (mm) of the cable CD.3.Calculate the vertical displacement of point C, in mm.ANSWERS: (1) 6 mm, (2) 1.186 mm, (3) 1.337 mm--

1. Derive an expression for H(w) filter or bandpass/reject filter. = for the circuit below. Qualitatively determine if it's a high/lowpass L ell R ww Vo

2. Obtain the transfer function, H(w) = 0 for the circuit below for R₁ = 1 kQ2, R2 = 10 kQ, and Vi C = 1 μF. What role, if any, does the capacitor play? Explain. R₁ R2 + C + Vo

Chapter 16 Solutions

EP ENGR.MECH.:DYNAMICS-STANDALONE ACC.

Ch. 16.3 - Determine its constant angular acceleration and...Ch. 16.3 - Determine the angular acceleration when it has...Ch. 16.3 - Determine the time it takes to achieve an angular...Ch. 16.3 - If the angular displacement of the wheel is =...Ch. 16.3 - Determine the magnitude of the velocity and...Ch. 16.3 - Determine the velocity of the cylinder and the...Ch. 16.3 - Determine the magnitudes of the velocity and...Ch. 16.3 - If the disk is originally rotating at 0 = 12...Ch. 16.3 - It it is subjected to a constant angular...Ch. 16.3 - If it is subjected to a constant angular...

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 relative velocity and relative acceleration of B with respect to A .

Solution Summary: The author analyzes the relative velocity and relative acceleration of B with respect to A.

Concept explainers

Videos

The relative velocity and relative acceleration of B with respect to A .

Want to see the full answer?

Chapter 16 Solutions