Download presentation

1
**Chapter 2 STATICS OF PARTICLES**

Forces are vector quantities; they add according to the parallelogram law. The magnitude and direction of the resultant R of two forces P and Q can be determined either graphically or by trigonometry. R P A Q Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2
Any given force acting on a particle can be resolved into two or more components, i.e.., it can be replaced by two or more forces which have the same effect on the particle. A force F can be resolved into two components P and Q by drawing a parallelogram which has F for its diagonal; the components P and Q are then represented by the two adjacent sides of the parallelogram and can be determined either graphically or by trigonometry. Q F A P

3
**F = Fx i + Fy j Fx = F cos q Fy = F sin q Fy tan q = Fx F = Fx + Fy 2**

A force F is said to have been resolved into two rectangular components if its components are directed along the coordinate axes. Introducing the unit vectors i and j along the x and y axes, F = Fx i + Fy j y Fx = F cos q Fy = F sin q tan q = Fy Fx Fy = Fy j F j F = Fx + Fy 2 q x i Fx = Fx i

4
**Rx = S Rx Ry = S Ry Ry tan q = R = Rx + Ry 2 Rx**

When three or more coplanar forces act on a particle, the rectangular components of their resultant R can be obtained by adding algebraically the corresponding components of the given forces. Rx = S Rx Ry = S Ry The magnitude and direction of R can be determined from tan q = Ry Rx R = Rx + Ry 2

5
**Fx = F cos qx Fy = F cos qy Fz = F cos qz Fy Fy qy F F qx Fx Fx Fz Fz**

B B Fy Fy qy A F A F D D O O qx Fx Fx x x Fz Fz E E C C z z y A force F in three-dimensional space can be resolved into components B Fy F Fx = F cos qx Fy = F cos qy A D O Fz = F cos qz Fx x qz E Fz C z

6
**F = F (cosqx i + cosqy j + cosqz k )**

l (Magnitude = 1) The cosines of qx , qy , and qz are known as the direction cosines of the force F. Using the unit vectors i , j, and k, we write Fy j F = F l cos qy j Fx i cos qz k x Fz k F = Fx i + Fy j + Fz k cos qx i z or F = F (cosqx i + cosqy j + cosqz k )

7
**l = cosqx i + cosqy j cos2qx + cos2qy F = Fx + Fy + Fz 2 cosqx = Fx F**

l (Magnitude = 1) cos qy j l = cosqx i + cosqy j + cosqz k Fy j cos qz k F = F l Since the magnitude of l is unity, we have Fx i x cos2qx + cos2qy + cos2qz = 1 Fz k z cos qx i In addition, F = Fx + Fy + Fz 2 cosqx = Fx F cosqy = Fy F cosqz = Fz F

8
**MN = dx i + dy j + dz k MN 1 l = = ( dx i + dy j + dz k ) d y**

A force vector F in three-dimensions is defined by its magnitude F and two points M and N along its line of action. The vector MN joining points M and N is N (x2, y2, z2) F dy = y2 - y1 l dz = z2 - z1 < 0 dx = x2 - x1 M (x1, y1, z1) x z MN = dx i + dy j + dz k The unit vector l along the line of action of the force is l = = ( dx i + dy j + dz k ) MN 1 d

9
**F = F l = ( dx i + dy j + dz k ) F d Fdx d Fdy d Fdz d Fx = Fy = Fz =**

d = dx + dy + dz 2 2 2 N (x2, y2, z2) dy = y2 - y1 A force F is defined as the product of F and l. Therefore, dz = z2 - z1 < 0 dx = x2 - x1 M (x1, y1, z1) x z F = F l = ( dx i + dy j + dz k ) F d From this it follows that Fdx d Fdy d Fdz d Fx = Fy = Fz =

10
When two or more forces act on a particle in three-dimensions, the rectangular components of their resultant R is obtained by adding the corresponding components of the given forces. Rx = S Fx Ry = S Fy Rz = S Fz The particle is in equilibrium when the resultant of all forces acting on it is zero.

11
**S Fx = 0 S Fy = 0 S Fz = 0 S Fx = 0 S Fy = 0**

To solve a problem involving a particle in equilibrium, draw a free-body diagram showing all the forces acting on the particle. The conditions which must be satisfied for particle equilibrium are S Fx = S Fy = S Fz = 0 In two-dimensions , only two of these equations are needed S Fx = S Fy = 0

Similar presentations

Presentation is loading. Please wait....

OK

Forces and equilibrium

Forces and equilibrium

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on modernization in indian railways Download seminar ppt on android Download ppt on area of circle Ppt on types of forest in india Ppt on history of atom timeline Ppt on osteoporosis Ppt on mars one mission Ppt on area of parallelogram and triangles in geometry Ppt on modern olympic games Presentations ppt online ticket