Question

What is the relationship between balanced force and net force?

Answer 1

Hint: A set of forces on a body is said to be a balanced force set, if the vector sum of all these forces comes out to be zero. Whereas, net force on a body is the sum of all these vector forces. We shall see the relationship between a balanced force and a net force and also see the conditions in which these relationships work.

Complete step-by-step answer:
Let us derive the relationship between the balanced force and the net force with the help of an example.
Let us say there is an object such that ‘n’ number of forces (some of them same, some different) are acting on the object simultaneously. This can be understood with the help of the following diagram:

Here, the sum of all the forces acting on the body can be written as:
$\Rightarrow \overrightarrow{{{F}_{net}}}=\overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}+\overrightarrow{{{F}_{4}}}+\overrightarrow{{{F}_{5}}}+\overrightarrow{{{F}_{6}}}+.........................+\overrightarrow{{{F}_{n}}}$
The term written in the Left-Hand Side of the above equation, that is, ‘$\overrightarrow{{{F}_{net}}}$’ is the sum of all the force vectors. This term is known as the net force on the body or the system.
Now, a balanced force is a special type of net force and is used when the net force on the system is equal to zero. Thus, in our above mathematical expression, if we had:
$\Rightarrow \overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}+\overrightarrow{{{F}_{4}}}+\overrightarrow{{{F}_{5}}}+\overrightarrow{{{F}_{6}}}+.........................+\overrightarrow{{{F}_{n}}}=0$
Then, we could say that:
$\Rightarrow \overrightarrow{{{F}_{net}}}=0$
Then, the term ‘$\overrightarrow{{{F}_{net}}}$ ’ is converted into ‘$\overrightarrow{{{F}_{balanced}}}$’ and we say that the net force in balanced.
Hence, the relationship between balanced force and net force is that they are equal (equal to zero) when the sum of net forces is zero and are undefined when the sum of forces in non-zero as balanced force has no meaning in such case.

Note: All balanced forces can be termed as net force but all net forces are balanced, need not be true. This is the simplest way to understand the difference in the basic meanings of the two terms. These two terms are commonly used in problems in Physics, so one should understand the difference in meanings of these terms carefully.