Question

Forces of magnitudes 1 N, 2 N, 3 N and 4 N are
acting along sides AB, CB, DC and DA of a
rectangle respectively. The magnitude of
resultant is
​

Answer 1

Given:

F1 = 1 N

F2 = 2 N

F3 = 3 N

F4 = 4 N

To find:

resultant R =?

Explanation:

The resultant of 4 vectors in X, Y directions are:

The resultant in the X direction  (+ve x-axis) is

$\vec{3P} - \vec{P} = \vec{2P}$

The resultant in the Y direction  (+ve y-axis) is

$\vec{4P} - \vec{2P} = \vec{2P}$

The net resultant force vector is the sum of the resultant force vector in the X direction & the resultant force vector in the Y direction.

∴$\vec{R} = \vec{2P} + \vec{2P}$

The angle between two vectors is 90°.

i.e. θ =  90°.

The magnitude of the resultant force vector is given by

$R = \sqrt{2^2 + 2^2+ 2\times2\times 2\ cos90 }$

R = 2$\displaysyle \mathbf{\sqrt{2}}$

The magnitude of the resultant force vector lies in the IV quadrant.

Refer to the following attachment:

Answer 2

Answer:6 n

Explanation: