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# Applying Newton's Three Laws

### Contents

#### Tension Force

The final common application of Newton's Laws deals with tension. Tension usually arises in the use of ropes or cables to transmit a force. Consider a block being pulled by a rope. The person doing the pulling at one end of the rope is not in contact with the block, and cannot exert a direct force on the block. Rather a force is exerted on the rope, which transmits that force to the block. The force experienced by the block from the rope is called the tension force.

Almost all situations you will be presented with in classical mechanics deal with massless ropes or cables. If a rope is massless, it perfectly transmits the force from one end to the other: if a man pulls on a massless rope with a force of 10 N the block will also experience a force of 10 N. An important property of massless ropes is that the total force on the rope must be zero at all times. To prove this, we go back to Newton's Second Law. If a net force acts upon a massless rope, it would cause infinite acceleration, as a = F/m, and the mass of a massless rope is 0. Such a situation is physically impossible and, consequently, a massless rope can never experience a net force. Thus all massless ropes always experience two equal and opposite tension forces. In the case of a man pulling a block with a rope, the rope experiences a tension in one direction from the pull of the man, and a tension in the other direction from the reactive force of the block:

Figure %: The Tension in a Massless Rope

#### Tension and Pulleys

The dynamics of a single rope used to transmit force is clearly quite simple: the rope just transmits an applied force. When pulleys are used in addition to ropes, however, more complicated situations can arise. In a dynamical sense, pulleys simply act to change the direction of the rope; they do not change the magnitude of the forces on the rope. Just as we assumed the ropes to be massless, we will similarly assume that the pulleys we work with are massless and frictionless, unless told otherwise. The simplest case involving a pulley involves a block being lifted by another block connected to a rope:

Figure %: The Tension in a Rope and Pulley System
This diagram represents a small block on the left in the act of being lifted by a larger block on the right. Notice the forces T and -T: even when used in addition to a pulley, the rope must still experience two equal and opposite tension forces. From the figure it may seem that the rope actually experiences two forces in the same direction, making the situation impossible. The presence of the pulley, however, changes the situation to make it physically tenable. When analyzing a rope and pulley situation it is useful to define a direction not in terms of up or down, but in terms of the shape of the rope. In the situation above, we can define the positive direction on the rope as pointing upward on the left side of the pulley, and pointing downward on the right side. When we define direction in this way the rope does actually experience two equal and opposite forces.