ilovepdf.com_split_6

# ilovepdf.com_split_6 - Chapter 4 Kinetics of a System of...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 4 Kinetics of a System of Particles Question 41 A particle of mass m is connected to a block of mass M via a rigid massless rod of length l as shown in Fig. P4-1. The rod is free to pivot about a hinge attached to the block at point O . Furthermore, the block rolls without friction along a horizontal surface. Knowing that a horizontal force F is applied to the block and that gravity acts downward, determine a system of two differential equations describing the motion of the block and the particle. F g l m x M O P Figure P4-1 130 Chapter 4. Kinetics of a System of Particles Solution to Question 41 Kinematics Let F be a reference frame fixed to the block. Then, choose the following coordinate system fixed in reference frame F : Origin at O at t = E x = To the Right E z = Into Page E y = E z E x Next, let A be a reference frame fixed to the rod. Then, choose the following coordinate system fixed in reference frame A : Origin at O e r = Along OP e z = Into Page e = E z e r We note that the relationship between the basis { E x , E y , E z } and { e r , e , e z } is given as E x = sin e r + cos e (4.1) E y = - cos e r + sin e (4.2) Also, we have that e r = sin E x- cos E y (4.3) e = cos E x + sin E y (4.4) Using the bases { E x , E y , E z } and { e r , e , e z } , the position of the block is given as r O = x E x (4.5) Then the velocity and acceleration of the block in reference frame F are given, respec- tively, as F v O = x E x (4.6) F v O = x E x (4.7) Next, the position of the particle is given as r = r P = r O + r P/O = x E x + l e r (4.8) Next, the angular velocity of reference frame A in reference frame F is given as F A = e z (4.9) 131 The velocity of point P in reference frame F is then given as F v P = F d dt ( r O ) + F d dt ( r P/O ) = F v O + F v P/O (4.10) Now we already have F v O from Eq. (4.6). Next, since r P/O is expressed in the basis { e r , e , e...
View Full Document

## This note was uploaded on 04/03/2012 for the course AERO 310 taught by Professor Chakravorty during the Spring '07 term at Texas A&M.

### Page1 / 7

ilovepdf.com_split_6 - Chapter 4 Kinetics of a System of...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online