Question

Two forces of 12 N and 25 N act on a body to the left hand side, while another force of 35 N acts on it to the right hand side. Find the resultant of the forces.

Answer 1

In such type of questions, vector logic is applied , according vector law of algebra any two vector are found in same direction then magnitude of resultant is obtained by adding them and its direction is same as the given vectors if two vectors are in opposite direction then magnitude of resultant is obtained by subtracting them and direction of resultant is in the direction of larger magnitude.

Complete step-by-step solution:
According to the question , we will consider a body as shown in the figure below on which 12N and 25N are acting on the left side of the body, While 35N is acting on the right side of the body.

Since force is the vector quantity, these forces are solved with the help of the vector concept.
As we know that in vector addition if vectors are found in the same direction then the magnitude of resultant can be obtained by adding them and if vectors are found in opposite direction then the magnitude of resultant is obtained by subtracting them.
Here,
two forces on the left side are in the same direction so their resultant is obtained by adding them.
So Force on the left becomes 37N

& {{F}_{Left}}=12+25 \\\ & {{F}_{Left}}=37N \\\ \end{aligned}$$. The direction of net force of the left is taken in the same direction of given forces. In the right only one force is acting so let us assume the force is $${{F}_{Right}}$$. So, $${{F}_{Right}}=35N$$. Now on the left side of the body 37N is acting and on the right side of the body 35N is acting. Since these forces are opposite in direction so their magnitude is obtained by subtracting the two forces which means larger force is subtracted from smaller force and direction of net force is along the larger force. So, $${{F}_{net}}={{F}_{Left}}-{{F}_{Right}}$$ $$\begin{aligned} & \Rightarrow {{F}_{net}}=37-35 \\\ & \therefore {{F}_{net}}=2N \\\ \end{aligned}$$. So it is concluded that the resultant of the force acting on the body is 2N and its direction is taken along the left side because the force of the left side is of greater magnitude than the force of the right side. **Note:** Any physics quantity having magnitude , direction and following vector laws of algebra is defined as vector quantity, only magnitude and direction is not sufficient for defining a vector. So any quantity following all three conditions is only called a vector quantity. Vector laws of algebra are entirely different from scalar laws of algebra.