Question

determine the resultant of 3 forces acting on a hook as shown inthe figure​

Answer 1

To find:

Resultant of the three forces?

Calculation:

First of all, we will divide the vectors in their components:

$\vec{F1} = 70 \cos( {50}^{ \circ} ) \hat{i} + 70 \sin( {50}^{ \circ} ) \hat{j}$

$\implies \vec{F1} = 44.9 \hat{i} + 53.6 \hat{j}$

Now, the second vector:

$\vec{F2} = 80 \cos( {25}^{ \circ} ) \hat{i} + 80 \sin( {25}^{ \circ} ) \hat{j}$

$\implies \vec{F2} = 72.5 \hat{i} + 33.8 \hat{j}$

Now, the third vector:

$\vec{F3} = 50 \cos( {45}^{ \circ} ) \hat{i} - 50 \sin( {45}^{ \circ} ) \hat{j}$

$\implies \vec{F3} = 35.36 \hat{i} - 35.36\hat{j}$

Now, resultant will be :

$\vec{F} = \vec{F1} + \vec{F2} + \vec{F3}$

$\implies \vec{F} = 152.76 \hat{i} - 52.04\hat{j}$

$\implies | \vec{F}| =161.3 \: N$

So, net magnitude of force is 161.3 N.