Question

Two forces of \[6\,{\text{N}}\] and \[8\,{\text{N}}\] can be applied to produce an effect of a single force of:
A. \[1\,{\text{N}}\]
B. \[15\,{\text{N}}\]
C. \[11\,{\text{N}}\]
D. \[20\,{\text{N}}\]

Answer 1

Hint: Two forces can yield maximum value if the two forces are applied in the same direction which is given by the arithmetic sum of the individual forces. Minimum value is obtained if the two forces are applied in the opposite direction which is given by the difference of the individual forces.

Complete step by step answer:
In the given question, we are supplied with the following data:
There are two forces \[6\,{\text{N}}\] and \[8\,{\text{N}}\].We are asked to find out the force which both of them combinedly produce as an effect of single force.

To begin with, we must know that force is a vector quantity, which has both magnitude and direction. Both the forces can be applied in such a way that it can have maximum magnitude and minimum magnitude. It all depends on the orientation of the forces at the point of application.

We can find out the maximum value of the resultant force by adding the two individual forces.
${F_{\max }} = {F_1} + {F_2} \\
\Rightarrow {F_{\max }} = 8 + 6 \\
\Rightarrow {F_{\max }} = 14\,{\text{N}} $
The maximum magnitude of the two forces is \[14\,{\text{N}}\].

We can find out the minimum value of the resultant force by subtracting the two individual forces.
${F_{\min }} = {F_1} - {F_2} \\
\Rightarrow {F_{\min }} = 8 - 6 \\
\therefore {F_{\min }} = 2\,{\text{N}} \\$
The minimum magnitude of the two forces is \[2\,{\text{N}}\].
So, the force which both of them combinedly produce as an effect of a single force will lie in the range between \[2\,{\text{N}}\] and \[14\,{\text{N}}\]. Hence, the required force is \[11\,{\text{N}}\].

The correct option is C.

Note: It is important to remember that force is a vector quantity as it has both the magnitude and the direction. The resultant force solely depends on the orientation of the forces applied at a particular point. The two forces will have maximum magnitude if the two forces are applied in the same direction which means the angle between them is \[0^\circ \]. The two forces will have minimum magnitude if the two forces are applied in the opposite direction which means the angle between them is \[180^\circ \].