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Tension is simply a specific name for the force exerted by a string or rope A simplification within this textbook is the assumption that all strings and ropes are massless To understand tension in more detail, consider the situation in Figure 4-14, where a bucket hangs from a rope attached to the ceiling The rope is about to break in the middle If the rope breaks, the bucket will fall; thus, before it breaks, there must be forces holding the rope together The force that the top part of the rope exerts on the bottom part is Ftop on bottom Newton s third law states that this force must be part of an interaction pair The other member of the pair is the force that the bottom part exerts on the top, Fbottom on top These forces, equal in magnitude but opposite in direction, also are shown in Figure 4-14 Think about this situation in another way Before the rope breaks, the bucket is in equilibrium This means that the force of its weight downward must be equal in magnitude but opposite in direction to the tension in the rope upward Similarly, if you look at the point in the rope just above the bucket, it also is in equilibrium Therefore, the tension of the rope below it pulling down must be equal to the tension of the rope above it pulling up You can move up the rope, considering any point in the rope, and see that the tension forces are pulling equally in both directions Because the very bottom of the rope has a tension equal to the weight of the bucket, the tension everywhere in the rope is equal to the weight of the bucket Thus, the tension in the rope is the weight of all objects below it Because the rope is assumed to be massless, the tension everywhere in the rope is equal to the bucket s weight Tension forces also are at work in a tug-of-war, like the one shown in Figure 4-15 If team A, on the left, is exerting a force of 500 N and the rope does not move, then team B, on the right, also must be pulling with a force of 500 N What is the tension in the rope in this case If each team pulls with 500 N of force, is the tension 1000 N To decide, think of the rope as divided into two halves The left-hand end is not moving, so the net force on it is zero Thus, FA on rope Fright on left 500 N Similarly, FB on rope Fleft on right 500 N But the two tensions, Fright on left and Fleft on right, are an interaction pair, so they are equal and opposite Thus, the tension in the rope equals the force with which each team pulls, or 500 N To verify this, you could cut the rope in half, tie the ends to a spring scale, and ask the two teams each to pull with 500 N of force You would see that the scale reads 500 N.

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