Question

Three concurrent forces are applied to keep 160N weight equilibrum. Two of the forces are given F1= (-2i-24j+11k)N and F2=13i+15j+85k)N. Assuming that the forces of gravity is along the z-axis, determine the components of the third force

Answer 1

Given:

Three concurrent forces are applied to keep 160N weight equilibrum. Two of the forces are given F1= (-2i-24j+11k)N and F2=13i+15j+85k)N. Forces of gravity is along the z-axis.

To find:

The components of the third force?

Calculation:

Since the object is in equilibrium, the force vectors will be balanced:

$\therefore \: \vec{F}_{1} + \vec{F}_{2} + \vec{F}_{3} = \vec{W}$

$\implies \: ( - 2 \hat{i} - 24 \hat{j} + 11 \hat{k}) + ( 13 \hat{i} + 15 \hat{j} + 85 \hat{k}) + \vec{F}_{3} = 160 \hat{k}$

$\implies \: ( 11 \hat{i} - 9\hat{j} + 96 \hat{k}) + \vec{F}_{3} = 160 \hat{k}$

$\boxed{\implies \: \vec{F}_{3} = - 11 \hat{i} + 9 \hat{j} + 64 \hat{k}}$

So, the components of F_(3) are:

• 11 N along -X axis

• 9 N along Y axis

• 64 N along Z axis