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Find the position of the centre of a sys...

Find the position of the centre of a system of parallel forces applied to a rigid body.

Text Solution

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The correct Answer is:
`x_(0)=(F_(1)x_(1)+F_(2)x_(2)+F_(3)x_(3)+……)/(F_(1)+F_(2)+F_(3)+….)`
Let the x-axis pass through the points of application of the forces, `A_(1)` and `A_(2)`, with the coordinates `x_(1)` and `x_(2)`, the coordinate of the centre O being `x_(0)`. Then `l_(1)=x_(0)-x_(1), l_(2)=x_(2) " " x_(0)`. Substituting this into the result of the previous problem, we obtain: `F_(1) (x_(0) - x_(1)) = `
`=F_(2)(x_(2)-x_(0))`, whence
`x_(0)= (F_(1)x_(1) +F_(2)x_(2))/(F_(1)+F_(2))`
The position of the centre of several parallel forces may be found by using the method of complete induction.
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