Question

Suppose 25 children who weigh the same are playing a game of tug of war, five children pull with 10 newtons of force, while ten children pull with 15 newtons of force in the opposite direction. How can one determine the net force on the rope?

Answer 1

To determine the net force on the rope, we need to find the vector sum of all the forces acting on it.

In this scenario, there are two groups of children pulling with different forces in opposite directions. The first group, consisting of five children, pulls with a force of 10 newtons. The second group, consisting of ten children, pulls with a force of 15 newtons in the opposite direction.

Since all the children in each group weigh the same, we can assume that each child in the first group contributes a force of 2 newtons (10 newtons divided by five children), while each child in the second group contributes a force of 1.5 newtons (15 newtons divided by ten children).

To find the net force, we sum up the forces in each direction.

For the first group, which is pulling towards the positive direction, the total force is:
5 children × 2 newtons/child = 10 newtons.

For the second group, which is pulling towards the negative direction, the total force is:
10 children × 1.5 newtons/child = 15 newtons.

To find the net force, we subtract the force in the opposite direction from the force in the positive direction:
Net force = 10 newtons - 15 newtons = -5 newtons.

Therefore, the net force on the rope is -5 newtons, indicating that the overall force direction is towards the negative side.