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Four forces act along the sides of a...

Four forces act along the sides of a smoth square frma ABCD in the order `A to B, B to C, C to D` and `D to A`. If the magnetiude of the force are `F_(1), F_(2), F_(3)` and `F_(4)` respectively, find the force acting on the frame . Assume `F_(1)= 1 N, F_(2) = 2 N, F_(3)= 3 N and F_(4) = N`

Text Solution

Verified by Experts

Let us consider x-y coordination system . The resultant of all the forces is
`vecF= vecF_(1) + vecF_(2) + vecF_(3) +vecF_(4)`
After bringing the tails of all the vectors to a point O and
substituting `vecF_(1) = 1 hati N`, `vecF_(2) = 2hatjN, vecF_(3) = - 3hati N` and
`vecF_(4) = - 4hatj N` we have
`" "vecF = - 2 (hati + hatj)N`

Henece the magntiude of `vecF`, that is , ` |vecF|= 2sqrt(2)` is directed in 3rd quadrant , as shown in the Fig. 3.39
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