The contact forces are referred to by different terms based on the nature of objects. If one of the forces in question that is the exerting object is a rope, cable or chain, it is referred to as tension.
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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.
The system of interest here is the point in the wire at which the tightrope walker is standing. As you can see in the figure, the wire is not perfectly horizontal it cannot be! Thus, the tension on either side of the person has an upward component that can support his weight. As usual, forces are vectors represented pictorially by arrows having the same directions as the forces and lengths proportional to their magnitudes.
The system is the tightrope walker, and the only external forces acting on him are his weight w and the two tensions T L left tension and T R right tension , as illustrated. It is reasonable to neglect the weight of the wire itself. The net external force is zero since the system is stationary. A little trigonometry can now be used to find the tensions. One conclusion is possible at the outset—we can see from part b of the figure that the magnitudes of the tensions T L and T R must be equal.
This is because there is no horizontal acceleration in the rope, and the only forces acting to the left and right are T L and T R. Thus, the magnitude of those forces must be equal so that they cancel each other out. Whenever we have two-dimensional vector problems in which no two vectors are parallel, the easiest method of solution is to pick a convenient coordinate system and project the vectors onto its axes.
In this case the best coordinate system has one axis horizontal and the other vertical. We call the horizontal the x -axis and the vertical the y -axis.
First, we need to resolve the tension vectors into their horizontal and vertical components. It helps to draw a new free-body diagram showing all of the horizontal and vertical components of each force acting on the system. Figure 7. When the vectors are projected onto vertical and horizontal axes, their components along those axes must add to zero, since the tightrope walker is stationary.
The small angle results in T being much greater than w. Now, observe Figure 7. You can use trigonometry to determine the magnitude of T L and T R. Notice that:. Now, considering the vertical components denoted by a subscript y , we can solve for T.
Thus, as illustrated in the free-body diagram in Figure 7,. Now, we can substitute the values for T L y and T R y , into the net force equation in the vertical direction:. Note that the vertical tension in the wire acts as a normal force that supports the weight of the tightrope walker. The tension is almost six times the N weight of the tightrope walker.
Since the wire is nearly horizontal, the vertical component of its tension is only a small fraction of the tension in the wire. The large horizontal components are in opposite directions and cancel, and so most of the tension in the wire is not used to support the weight of the tightrope walker.
If we wish to create a very large tension, all we have to do is exert a force perpendicular to a flexible connector, as illustrated in Figure 8. As we saw in the last example, the weight of the tightrope walker acted as a force perpendicular to the rope. We saw that the tension in the roped related to the weight of the tightrope walker in the following way:. Even the relatively small weight of any flexible connector will cause it to sag, since an infinite tension would result if it were horizontal i.
See Figure 8. Figure 8. We can create a very large tension in the chain by pushing on it perpendicular to its length, as shown. Suppose we wish to pull a car out of the mud when no tow truck is available. Each time the car moves forward, the chain is tightened to keep it as nearly straight as possible. Figure 9. Unless an infinite tension is exerted, any flexible connector—such as the chain at the bottom of the picture—will sag under its own weight, giving a characteristic curve when the weight is evenly distributed along the length.
Suspension bridges—such as the Golden Gate Bridge shown in this image—are essentially very heavy flexible connectors. The weight of the bridge is evenly distributed along the length of flexible connectors, usually cables, which take on the characteristic shape. There is another distinction among forces in addition to the types already mentioned. Does Tension Depend on Mass? If weight is hanged from a cable or wire from a fixed point, the wire or cable would be under tension proportional to the mass of the object.
The wire is under tension proportional to the force of pulling. Tension usually arises in the use of cables, rope to transmit a force. The person pulling at one end of the rope is not in contact with the block in the other end and cannot exert the direct force on the block. So, the force is exerted on the rope, which transmits the force to the block. The force that is experienced by the block from the rope is called the tension force.
The classical mechanics deal with massless ropes or cables. If a cable or rope is massless, then it perfectly transmits the force from one end to another end.
For example, if a man pulls the massless rope with a force of 30 N then the block will also experience the force of 30 N only. An important property of the massless rope should be that the total force on the rope must be zero at all times. The situation mentioned above is not physically possible and consequently, the massless rope can never experience the net force.
Thus, all the massless rope will experience the two equal and opposite tension forces. Tension and Pulleys:. The dynamics of a single rope is quite simple and easy as it transmits the applied force.
But when pulleys are used instead of ropes then the complications arise. In the dynamical sense, the pulleys act to change the direction of the rope and they do not change the magnitude of the forces on the rope.
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