Question

In a game of tug of war, three girls of team A pull the rope with forces of $100\,N$, $120\,N$ and $170\,N$. In team B, the three members pull the rope with forces of $130\,N$, $150\,N$ and $155\,N$. Who will win the tug of war? What is the resultant force?

Answer 1

Here we have to apply the concept of resultant forces. The resulting force is the single force obtained by integrating a system of forces and torques acting on a rigid body and the corresponding torque. The distinguishing characteristic of the resulting force, or the resulting force-torque, is that it has the same effect as the initial force mechanism on the rigid body.

Complete step by step answer:
The resultant force, and its orders, is nothing but the absolute force acting on a person. The corresponding force should be negligible if the target is at rest or travelling at the same velocity. All forces behave in the same way, and the sum of all forces should be the resulting force.
The forces applied by team A are: $100\,N$ , $120\,N$ and $170\,N$.
So, total force will be
${F_A} = 100 + 120 + 170 \\\ \Rightarrow{F_A} = 390\,N \\\$
The forces applied by team B are: $130\,N$ ,$150\,N$ and $155\,N$.
So, total force will be
${F_B} = 130 + 150 + 155 \\\ \Rightarrow{F_B} = 435\,N \\\$
So, the resultant force will be (as the forces are applied in opposite direction in tug of war):
$F = 435 - 390 \\\ \therefore F= 45\,N \\\$
Hence, team B will win the game as they have applied an additional force of $45\,N$.

Additional information:
A force is a push or pull on an object that results from the contact of the object with another object. There is a force on each of the objects if there is an interaction with two objects.
The speed and trajectory of a moving target can also be modified by force. When force is applied to an object, resulting in the object's movement, it is said that work is finished.

Note: We should not be confused between single force and resultant force. The result is a single force that, both in magnitude and direction, can replace the entire system of forces. If, moreover, another force is applied to the body, similar to the resultant in its magnitude and opposite the direction of the resultant, so the body comes to rest.