The Question: Let’s suppose that Myrtle and Bernie are pulling on a rope toward the west. Myrtle pulls with a force of 50 pounds while Bernie pulls with a force of 70 pounds. This game of tug of war is only among three (former) friends and Chester is on the other side pulling directly to the east. What minimum force must Chester exert in order to win the game?
The Answer:
You know the answer: the eastern-pulling team exerts a total of pounds of force and so Chester must pull with any amount over pounds in the other direction. In symbols, our Newton 2nd law statement says that for balance:
So pounds wins. Or pounds. Or even pounds. Notice that the negative signs signify that I’ve designated east as the positive direction, so vectors are implied but not explicitly designated.