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P a Force of 100 N Acts at a Point P(-2,3,5)M Has Its Line of Action Passing Through Q(10,3,4)M. Calculate Moment of this Force About Origin (0,0,0). - Engineering Mechanics

A Force of 100 N acts at a point P(-2,3,5)m has its line of action passing through Q(10,3,4)m. Calculate moment of this force about origin (0,0,0).

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Solution

Given: O = (0,0,0) 

P= (4.5, -2) Q= (-3,1,6) A= (3,2,0) F=100 N To find : Moment of the force about origin

Solution: Let 𝑝̅ and 𝑞 ̅be the position vectors of points P and Q with respect to the origin 0 

∴` baro9=bar(-2l)+3J+5k`

∴` bar oQ=10barl+3barJ+4k` 

∴ `bar(PQ)=bar(oQ)-bar(oP)=(10barl+3barJ4bark)-(-2barl-3barJ+5k)` 

=`12barl-bark`

∴ `|pQ| I=sqrt(12^2+(-1)^2)=sqrt145` 

Unit vector along`PQ= bar(PQ)=bar(PQ)/|bar(PQ)|=(12barl-bark)/sqrt145` 

Force along `PQ=barf=100xx(12barl-bark)/sqrt145`

Moment of F about O = `bar(OP)xxbarf`

                                                       `barl   bar J  bark`

                          `=100/sqrt145 xx -2   3   5  `

                                                    ` 12    0  -1` 

                                =`8.3045 (-3bari+58barj-36-bark)` 

             =`-24.9135barj+481.661.66barj-298.962bark Nm` 

Moment of the force =`-24.9135barj+481.661.66barj-298.962bark Nm` 

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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