# ENGG 202 Lecture Notes - Lecture 1: Unit Vector, Cross Product, Harmonic Oscillator

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Published on 26 Jan 2015

School

Department

Course

Professor

ENGG 202 Winter 2013 Tutorial 6 February 12/13, 2013

10 N-m

2 m

4 m

30 N

30 N

5

12

5

12 AB

C

D

Moment of a couple

1) The two couples act on a rectangular plate as shown

below. a) Determine the single equivalent couple acting

on the plate. b) Determine the direction and magnitude

of a horizontal force exerted at B so that the resultant

moment of all the forces about point D is zero.

ANS: a) M =

97.7 N-m CW,

b) FB = 48.8 N

left

Solution Strategy: part a) 1 couple is shown as a pair of

forces, the other is represented by its moment. To find

the single equivalent couple (or moment) acting on the

plate, we simply need the total moment acting on the

plate since the sum of the forces will be zero (only

couples acting on it). So calculate the moment of the 30

N couple either by summing moments about a point, or

by determining the perpendicular distance between the

two lines of action and then multiplying by the force magnitude, or by resolving each 30 N force

into x and y components (giving you two couples to replace the one) and calculating the moments

due to each couple (x comps and y comps) and adding them.

Part b) draw a horizontal force at B, (assume the direction right or left as you wish). Then sum

the moments about point D to find the magnitude of this force. Since you already calculated the

total moment due to the couples in part a) then the sum of moments (which must equal 0) is the

moment due to the force you added at B plus the total moment from part a) (couples are free

vectors so the moment must be applied everywhere and is the same everywhere)

2) What is the magnitude of the forces that must be

applied at A and B if the moment of the couple must

have a magnitude of 600 N-m. ANS: 1488.4N

Solution Strategy: You can use vectors to solve: |rAB x F| = 600 Nm, or use the scalar definition

of the moment for the couple. The diagonal distance AB is the distance that is perpendicular to

both lines of action (vertical lines) so

600 = Fd, calc the diagonal distance d and you can solve for F.