A recent browse of photo albums reminds me of the tug of war in my senior year at my high school. Unfortunately, our class lost during that game. At that time, we only thought that we didn’t have enough strong people and good strategies. But after this semester’s learning, it motivates me to take a deep analysis of tug of war based on physics.
We usually believe that tug of war is about strength. However, after drawing the free body diagram, I realize that tug of war is not really about strength but about friction. If you don’t have enough friction, it doesn’t matter how strong you are because you will slide all the way.
From the third Newton's law we know that if two objects interact, they apply forces to each other of equal magnitude and opposite direction. Since the person pulls on the rope, the rope pulls on the person in the opposite direction. So if you were to increase your force on the rope to 2,000 Newtons, the same rope pulls on both people. So how much force you apply is not the key point here.
Each puller has basically four forces acting on them: tension from rope, friction from ground, weight, and normal frounce from ground. Two vertical forces get canceled. Therefore, if a puller wants to win, his friction force must outweigh the tension from rope.
But it is still about mass!!
From previous learning, we know that friction force is equal to normal force x friction coefficient. With more mass, people will have more weight based on the equation of Fg = mg. The magnitude of normal force is equal to the magnitude of weight since the acceleration in vertical direction is zero. Therefore, with more mass, people will have greater normal force, resulting in greater friction force. Probably that is the reason why people want strong and heavy pullers to join the team. Meanwhile, strength may refer to great friction force here based on the explanation.
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