Four boys participate in the tug-of-war competition. to the left, two boys pull the rope with forces

Four boys participate in the tug-of-war competition. to the left, two boys pull the rope with forces of 530 N and 540 N, respectively, and to the right, two boys pull the rope with forces of 560 N and 520 N, respectively. in which direction and with what resultant force will the rope be pulled?

Given:

F1 = 530 Newton – the force with which the first boy pulls the rope (to the left);

F2 = 540 Newton – the force with which the second boy pulls the rope (to the left);

F3 = 560 Newton – the force with which the third boy pulls the rope (to the right);

F4 = 520 Newton – the force with which the fourth boy pulls the rope (to the right).

It is required to determine F (Newton) – the resultant of forces, as well as its direction.

Let us introduce a coordinate system, the positive OX direction of which will be directed to the right.

Then, according to Newton’s third law, we have:

F = -F1 – F2 + F3 + F4 = -530 – 540 + 560 + 520 = -1070 + 1080 = 10 Newtons.

Since the value of the resultant force has a positive sign, it means that it will be directed to the right.

Answer: the rope will be pulled to the right with a net force equal to 10 Newtons.