Question

Find the resultant and direction of 15n and 20n acting with the horizontal

Answer 1

Explanations & Calculations

• Since both forces are acting with the horizontal, the direction of the resultant lies along the horizontal, but where it directs depends on how the forces act on the body.

• The resultant is obtained by considering the vector addition.

• When both forces heading the same direction, the resultant is the addition of them which in this case gives, $\small R=\overrightarrow{15}\,N+\overrightarrow{20}\,N=\,\overrightarrow{35}\,N$
• The direction of the resultant is the same as those of the 2 forces
• This orientation of forces gives the largest possible resultant of a given set of forces.

• When the forces are acting opposite to each other, the resultant is given by the subtraction of them & the direction is set to that of the largest force. For the given case,

$\qquad\qquad \begin{aligned} \small R_1&= \small \,\overrightarrow{20}\,N+\overleftarrow{15}\,N\\ &= \small\,\overrightarrow{20}\,N-\overrightarrow{15}\,N\\ &= \small \overrightarrow{5}\,N \end{aligned}$

• This orientation gives smallest possible value for the resultant.