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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 alongPQ= 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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