Explanation Given: The angular velocity of the arm A B is ω A B = 5 rad/s (counter clockwise). The angular acceleration of the arm A B is α A B = 2 rad/s 2 . The angular velocity of the grip B C relative to fixed reference is ω ' = 6 rad/s (clockwise). The angular acceleration of the grip B C relative to fixed reference is α ' = 2 rad/s 2 . Draw the free body diagram of system as shown in Figure 1. Refer Figure (1). Write the formula for velocity of the object measured from the x , y , z reference. v C = v B + Ω × r C / B + ( v C / B ) x y z (I) Here, v C velocity vector of object at C measured from the X , Y , Z reference, v B is the velocity vector of the origin B (end of the arm where the object is connected) measured from the X , Y , Z reference, ( v C / B ) x y z is the velocity vector of object at the grip C with respect to arm end B measured by an observer attached to the rotating x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r C / B is the position vector of the object at grip C with respect to arm end B . Write the formula for acceleration of the object measured from the x , y , z reference a C = a B + Ω ˙ × r C / B + Ω × ( Ω × r C / B ) + 2 Ω × ( v C / B ) x y z + ( a C / B ) x y z (II) Here, a C acceleration vector of object at C measured from the X , Y , Z reference, a B is the acceleration vector of the origin B (end of the arm where the object is connected) measured from the X , Y , Z reference, ( v C / B ) x y z , ( a C / B ) x y z is the velocity and acceleration vector of the object at grip C with respect to arm end B measured by an observer attached to the rotating x , y , z reference, Ω ˙ is the angular acceleration due to the rotation of x , y , z reference, Ω is the angular velocity of the x , y , z reference measured from the X , Y , Z reference and r C / B is the position vector of the object at grip C with respect to arm end B . Write the formula for velocity at B of the arm A B . v B = ω A B × r B / A (III) Here, ω A B is the angular velocity of the arm A B and r B / A is the position vector arm end B with respect to arm end A . Write the formula for acceleration at B of the arm A B . a B = α A B × r B / A − ω A B 2 r B / A (IV) Here, α A B is the angular acceleration of the arm A B . Conclusion: Refer Figure (1). Write the position vector ( r B / A ) directed from A to B . r B / A = ( 0.3 cos 30 ° ) i + ( 0.3 sin 30 ° ) j = 0 .2598i + 0.15 j Write the position vector ( r C / B ) directed from B to C . r C / B = ( 0.125 cos 15 ° ) i + ( 0.125 sin 15 ° ) j = 0.121 i + 0.0324 j The angular velocity vector of the arm A B is ω A B = 5 k (counter clockwise). The angular acceleration vector of the arm A B is α A B = 2 k (counter clockwise). Calculate the velocity at B of the arm A B . Substitute 5 k for ω A B and 0 .2598i + 0.15 j for r B / A in Equation (III). v B = 5 k × ( 0 .2598i + 0.15 j ) = | i j k 0 0 5 0.2598 0.15 0 | = i ( 0 − 0.75 ) − j ( 0 − 1.299 ) + k ( 0 − 0 ) = ( − 0.75 i + 1.299 j ) m/s Calculate the velocity at B of the arm A B . Substitute 2 k for α A B , 5 for ω A B and 0

14th Edition

ISBN: 9780133976588

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 142P

To determine

The velocity and acceleration of the object held at grip C .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.8, Problem 141P

Chapter 16.8, Problem 143P

Students have asked these similar questions

Recall that the CWH equation involves two important assumptions. Let us investigate how these assumptions affect the accuracy of state trajectories under the control inputs optimized in (a) and (b). (c.1): Discuss the assumptions about the chief and deputy orbits that are necessary for deriving CWH.

PROBLEM 2.50 1.8 m The concrete post (E-25 GPa and a = 9.9 x 10°/°C) is reinforced with six steel bars, each of 22-mm diameter (E, = 200 GPa and a, = 11.7 x 10°/°C). Determine the normal stresses induced in the steel and in the concrete by a temperature rise of 35°C. 6c " 0.391 MPa 240 mm 240 mm 6₁ = -9.47 MPa

For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to a(t) = a(0) exp(-4) (15.10) where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) after 30 s.

Chapter 16 Solutions

EP ENGR.MECH.:DYNAMICS-REV.MOD.MAS.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 velocity and acceleration of the object held at grip C .

Solution Summary: The author explains how to determine the velocity and acceleration of the object held at grip C.

Concept explainers

Videos

The velocity and acceleration of the object held at grip C .

Want to see the full answer?

Chapter 16 Solutions