(a) Explanation Given Information: The mass ( m ) of the sheet steel is 2.4 kg. The dimension of the sheet steel is 160mm X 640 mm. The component is at rest when a couple ( M 0 ) for is ( 0.8 N ⋅ m ) k is applied to it. Calculation: The system is split in three sections consisting of two square plates and a rectangular plate to calculate the area. Calculate the area ( A ) of the system using the relation: A = b 2 + ( 2 b ) b + b 2 Here, side is b . Substitute 160 mm for b . A = ( 160 mm ) 2 + ( 2 × 160 mm ) ( 160 mm ) + ( 160 mm ) 2 = 25 , 600 + 51 , 200 + 25 , 600 = ( 102 , 400 mm 2 ) ( m 2 10 6 mm 2 ) = 0.1024 m 2 Calculate the mass per unit area of the steel using the relation: ρ = m A Here, ρ is mass per unit area. Substitute 2.4 kg for m and 0.1024 m 2 for A . ρ = 2.4 kg 0.1024 m 2 = 23.4375 kg / m 2 Express the angular moment ( H G ) of the system about the mass centre. H G = − I x z ω i − I y z ω j + I z ω k Here, I x z is mass moment of inertia about xz axis, I y z is mass moment of inertia about yz axis, I z is mass moment of inertia about the z axis, and ω is angular velocity. The moment of inertia about the xz plane is zero. H G = − I y z ω j + I z ω k (1) Express the angular momentum ( H ˙ G ) G x y z of the reference frame Gxyz. ( H ˙ G ) G x y z = − I x z α i − I y z α j + I z α k Express the angular velocity of the reference frame Gxyz . Ω = ω k (2) Here, Ω is angular velocity of reference frame is. The moment of inertia ( H ˙ G ) G x y z about the xz plane is zero. ( H ˙ G ) G x y z = − I y z α j + I z α k (3) Express the rate of change of angular momentum. H ˙ G = ( H ˙ G ) G x y z + Ω × H G (4) Substitute Equation (1), (2), and (3) in Equation (4). H ˙ G = ( − I y z α j + I z α k ) + ω k × ( − I y z ω j + I z ω k ) The matrix multiplication for vector product is done. H ˙ G = − I y z α j + I z α k + I y z ω 2 i (5) Express the moment of inertia ( I z ) a r e a about the z axis. ( I z ) a r e a = plate A + plate A B + plate B = [ 1 6 b 4 + b 2 ( 1 2 b ) 2 ] + [ 1 12 ( 2 b ) b 3 ] + [ 1 6 b 4 + b 2 ( 1 2 b ) 2 ] = 1 6 b 4 + 1 4 b 4 + 1 6 b 4 + 1 6 b 4 + 1 4 b 4 = b 4 Express the moment of inertia ( I y z ) a r e a about the yz axis (b) To determine The dynamic reaction at A ( A) and B ( B ) immediately after the couple is applied.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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 18, Problem 18.152RP

(a)

To determine

The angular acceleration (α) of the component.

(b)

To determine

The dynamic reaction at A (A) and B (B) immediately after the couple is applied.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18, Problem 18.151RP

Chapter 18, Problem 18.153RP

Students have asked these similar questions

الثانية Babakt Momentum equation for Boundary Layer S SS -Txfriction dray Momentum equation for Boundary Layer What laws are important for resolving issues 2 How to draw. 3 What's Point about this.

R αι g The system given on the left, consists of three pulleys and the depicted vertical ropes. Given: ri J₁, m1 R = 2r; απ r2, J2, m₂ m1; m2; M3 J1 J2 J3 J3, m3 a) Determine the radii 2 and 3.

B: Solid rotating shaft used in the boat with high speed shown in Figure. The amount of power transmitted at the greatest torque is 224 kW with 130 r.p.m. Used DE-Goodman theory to determine the shaft diameter. Take the shaft material is annealed AISI 1030, the endurance limit of 18.86 kpsi and a factor of safety 1. Which criterion is more conservative? Note: all dimensions in mm. 1 AA Motor 300 Thrust Bearing Sprocket 100 9750 เอ

Chapter 18 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - Prob. 18.3P Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - A homogeneous disk of mass m = 8 kg rotates at the...Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Determine the angular momentum HO of the disk of...

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 angular acceleration ( α ) of the component.

Solution Summary: The author calculates the mass per unit area of the steel using the relation: rho =mA