Addition of forces on opposite directions

 

Statement

difficulty

A boy and a girl tight two cords to a ring and play to find out who is stronger. The boy grab one of the cords and exert a force of 11 N, the girl applies 13 N at the same time. If both pull the cords on different directions... Who will win?

Solution

Info

Fchico = 11 N
Fchica = 13 N

FR = ?

Resolution

Thus the forces exerted are concurrent and are applied on the same direction but opposite sense, both can be replaced by one and only resultant force. That force has the same direction than the bigger one. On this case:

FR = | Fboy - Fgirl |
FR = | 11 N - 13 N |
FR = 2 N

That means the equivalent situation is as the boy doen´t pull the cord and she would pull with a force of 2 N. So, the girl wins.

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
∑F→=F1→+F2→+F3→+...+Fn→
Resultant Force of a System of Forces

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Subject Newton's laws of motion
Section Resultant Force of a System of Forces