Explanation Calculation: Find the position vector of OA . O A → = 3 2 a i − 3 a j + 3 a k Find the magnitude of O A → using the relation as shown below: d O A = ( 3 2 a ) 2 + ( − 3 a ) 2 + ( 3 a 2 ) = ( 9 4 a 2 ) + ( 9 a 2 ) + ( 9 a 2 ) = 3 a 1 + 4 + 4 4 = 3 a 9 4 = 3 a 3 2 d O A = 9 a 2 Find the magnitude of λ O A as shown below: λ O A = 1 9 2 a ( 3 2 a i − 3 a j+3 a k ) = 2 9 a ( 3 2 a i − 3 a j+3 a k ) = 1 3 ( i − 2 j + 2 a k ) For a rectangular coordinate system with origin at point A and axes aligned with the given x , y , z axes. Refer to Figure 9.28 in section,”9.5E Moments of inertia of composite bodies” in the textbook. Express the moment of inertia about x and z axis of circular cone as shown below: I x = I z = 3 5 m [ 1 4 a 2 + ( 3 a ) 2 ] = 3 5 m [ 1 4 a 2 + 9 a 2 ] = 3 5 m [ 37 a 2 4 a 2 ] = 111 20 m a 2 Express the moment of inertia about y axis of circular cone as shown below: I y = 3 10 m a 2 As the symmetry implies I x y = I y z = I z x = 0 . Refer to Equation 9.46 in section, “9

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.6, Problem 9.163P

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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Chapter 9.6, Problem 9.162P

Chapter 9.6, Problem 9.164P

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Sign in PDF Lecture W09.pdf PDF MMB241 - Tutorial L9.pdf File C:/Users/KHULEKANI/Desktop/mmb241/MMB241%20-%20Tutorial%20L9.pdf II! Draw | I│Alla | Ask Copilot + of 4 D Topic: Kinetics of Particles: - Forces in dynamic system, Free body diagram, newton's laws of motion, and equations of motion. TQ1. The 10-kg block is subjected to the forces shown. In each case, determine its velocity when t=2s if v 0 when t=0 500 N F = (201) N 300 N (b) TQ2. The 10-kg block is subjected to the forces shown. In each case, determine its velocity at s-8 m if v = 3 m/s at s=0. Motion occurs to the right. 40 N F = (2.5 s) N 200 N 30 N (b) TQ3. Determine the initial acceleration of the 10-kg smooth collar. The spring has an unstretched length of 1 m. 1 σ Q ☆ Q 6 ا الى ☑

Sign in PDF Lecture W09.pdf PDF MMB241 - Tutorial L9.pdf File C:/Users/KHULEKANI/Desktop/mmb241/MMB241%20-%20Tutorial%20L9.pdf II! Draw | I│Alla | Ask Copilot + 4 of 4 | D TQ9. If motor M exerts a force of F (10t 2 + 100) N determine the velocity of the 25-kg crate when t kinetic friction between the crate and the plane are μs The crate is initially at rest. on the cable, where t is in seconds, 4s. The coefficients of static and 0.3 and μk = 0.25, respectively. M 3 TQ10. The spring has a stiffness k = 200 N/m and is unstretched when the 25-kg block is at A. Determine the acceleration of the block when s = 0.4 m. The contact surface between the block and the plane is smooth. 0.3 m F= 100 N F= 100 N k = 200 N/m σ Q Q ☆ ا الى 6 ☑

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Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A .

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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