EAS208_HW09_112910_Solutions

# EAS208_HW09_112910_Solutions - EAS 208(Fall 2010 Homework#9...

This preview shows pages 1–5. Sign up to view the full content.

EAS 208 (Fall 2010) Homework #9 – Solutions Problem 18–50 The slender bar and 0. cylindrical disk are released from rest with the bar horizontal. The disk rolls on the curved surface. What is the bar’s angular acceleration at the instant it is released? 0.1 kg 2 kg Answer: The F.B.D for the bar and the disk, at the instant shown, are shown in the figure below: 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Disk The equation of motion in the y -direction is: , , disk y disk disk y y disk disk disk y F m a f B W m a Σ = = , (1) The equation of rotational motion (take moments about the center of mass): disk disk disk M I α Σ = disk disk Rf I α = (2) The disk rolls, therefore the kinematic condition for its center is: , disk y disk a R α = − (3) Bar The equation of motion in the -direction is: y , , bar y bar bar y y y bar bar bar y F m a A B W m a Σ = + = , (4) The equation of rotational motion (take moments about the center of mass): bar bar bar M I α Σ = 2 2 bar bar y y bar bar l l A B I α + = (5) The kinematic conditions for the bar is found from the acceleration of the center of the mass of the bar relative to point A : , , bar y A bar bar y bar bar bar y A A r r α ω ω = + × + × × a a r r r r r , ( ) ( ) ( ) , 0 0 0 2 2 bar bar bar y bar l l α = + × + × × a k i k k r i , 2 bar bar y bar l α = a j or , 2 bar bar y bar l a α = (6) 2
From Eq. (1), Eq. (2) and Eq. (3): , 2 disk y disk disk disk y I B W m a R = + (7) From Eq. (4), Eq. (5) and Eq. (6): 2 bar bar y y bar bar m l A B W α + = (8) 2 2 bar bar y y bar bar l l A B I α + = (9) The kinematic condition for the disk and the bar is found from the acceleration of the center of the mass of the disk relative to point : A , , disk y A bar disk y bar bar disk y A A r r α ω ω = + × + × × a a r r r r r , ( ) ( ) ( ) ( ) ( ) ( ) , 0 0 0 disk y bar bar bar l l α = + × + × × a k i k k r i , disk y bar bar l α = a j or , disk y bar bar a l α = (10) From Eq. (7) and Eq. (10): 2 disk y disk disk bar bar I B W m l R α = + (11) We have the set of three equations Eq. (8), Eq. (9) and Eq. (11) and we have three unknowns y A , y B , and bar α : 2 2 2 2 2 2 2 2 12 2 bar bar bar bar y y bar bar y y bar bar bar bar bar bar bar bar y y bar bar y y bar disk disk y disk disk bar bar y disk disk bar bar m l m l A B W A B W l l l l m l A B I A B I m B W m l B W m l R α α α α α α + = + = + = + = = + = + 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
( ) 0.981 0.006 0.981 0.006 0.06 0.06 0.00012 0.06 0.06 0.00012 1.962 0.2 0.1 0.12 1.962 0.036 y y bar y y bar y y bar y y bar y bar y bar A B A B A B A B B B α α α α α α + = + = + = + = = + = − (1) (2) 61.3125 0.042 2.943 0.08 4.905 0.038 1.962 0.038 1.962 0.038 1.962 1.962 0.036 1.962 0.036 1.962 0.036 bar y bar bar y bar y bar y bar y bar y bar y b rad A s A A A B B B α α α α α α α α = − = = + = − + = − + = − = − = − = − ar α 61.3125 0.367875 0.24525 bar y y rad s A N B N α = − = =
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern