Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of...

Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of letters. Show that the system equivalent to a single force and find its magnitude, direction and line of action.

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aruv | High School Teacher | (Level 2) Valedictorian

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Forces of magnitude aF,bF,aF,bF and cF act respectively along the sides BA,BC,DC,DA and the diagonal BD of a rectangle ABCD, where a=AB, b=BC and c=BD, in the directions specified by the order of letters. Show that the system equivalent to a single force and find its magnitude, direction and line of action.

Consider a triangle BAD.Forces acting along a direction taken in order,along  BA is  aF ,along AD  -bF and along BD is cF. By triangle law, Resultant is

BD=BA+AD

cF=aF-bF            (i)

Consider a triangle BCD.Forces acting along a direction taken in order,along  BC is  bF ,along CD  -aF and along BD is cF. By triangle law, Resultant is

BD=BC+CD

cF=bF-aF             (ii)

From

(i) and (ii)

2cF=0

cF=0

=> resulatnt of the forces is zero.

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