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Statics(MCB 1053)

W02L1

TOC

• AOB

• week 2 outlook

• Chapter 2: Force Vectors

1Copyright © 2010 Pearson. (adapted by AAW)

AOB

• Week 1 Assignment (autodidactic):

 – F2-5, 2-19, 2-24, F2-12, 2-39, 2-56, 2-58

• Online assignments

 – for MasteringEngineering please use “official” UTP name & ID

 – practice assignments up until 11:59pm Wed this week – graded online assignments start in week 2 onwards

 – check the website regularly

• Tutorial

 – tutorial signup: Sections 1, 3, 4 already full

 – attend your own section only (for the entire semester)

• check for any announcements on UTP eLearning

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Week 2 outlook

• Chapter 2: Force Vectors

 – scalars and vectors

 – vector operation

 – vector addition of forces – addition of a system of 

coplanar forces

 – position vectors

 – force vectors directed

along a line

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• If the resultant force is required to act along the positive u axis andhave a magnitude of 5kN, determine the required magnitude of F B and its direction ! .

P2-8

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• The beam is to be hoisted using two chains. If the resultant force isto be 600 N directed along the positive y axis, determine themagnitudes of forces F A and F B acting on each chain and the angle ! .of F B so that the magnitude of F B is a minimum. F A acts 30o from the

 y axis as shown.

P2-29

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Chapter Objectives

• to use Parallelogram or Triangle Laws to add forces & resolveinto components

• to express forces & vectors in Cartesian Vector Notation (CVN) - today’s lecture

• to use Dot Product to determine angle between two vectors andthe projection of one vector onto another vector 

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Addition of a System of Coplanar Forces

• we can resolve a vector F into two components along twoperpendicular axes, x and y and write: F = F x + F y

• the x and y components are called rectangular components

• Scalar notation: since x and y axes are perpendicular:   F  x =  F cos !   and  F  y =  F sin ! 

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F y

• we can also define unit vectors i and j along the x and y axesrespectively

• these unit vectors are dimensionless and have a magnitude of 1

• Cartesian Vector Notation:

we write: F =  F  x i +  F  y j

Addition of a System of Coplanar Forces

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Addition of a System of Coplanar Forces

• Coplanar Force Resultants:

• Cartesian vector notation:

  F1 =  F 1 x i +  F 1 y j

  F2 = - F 2 x i +  F 2 y j  F3 =  F 3 x i -  F 3 y j

• resultant:

F R = ( F 1 x - F 2 x+ F 3 x )  i + ( F 1 y +  F 2 y -  F 3 y) j

• Scalar notation:

 !   F  Rx =  F 1 x - F 2 x+ F 3 x

  "   F  Ry =  F 1 y +  F 2 y -  F 3 y

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• Coplanar Force Resultants:

• generic case: F R =  F  Rx i +  F  Ry j

• magnitude of F R:

• direction:

Addition of a System of Coplanar Forces

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PF2-10

• If the resultant force acting on the bracket is to be 750 N directedalong the positive x axis, determine the magnitude of F and itsdirection ! .

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P2-49

• Determine the magnitude of the resultant force and its directionmeasured counterclockwise from the positive x axis.

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