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A tightly stretched "high wire" is 36 $\mathrm{m}$ long. It sags 2.1 $\mathrm{m}$when a $60.0-\mathrm{kg}$ tightrope walker stands at its center. What isthe tension in the wire? Is it possible to increase the tensionin the wire so that there is no sag?

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$2500 \mathrm{N}$ It is not possible to increase the tension so that there is no sag.

Physics 101 Mechanics

Chapter 12

Static Equilibrium; Elasticity and Fracture

Equilibrium and Elasticity

Cornell University

University of Washington

Hope College

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

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glow on for particle direction for the equilibrium conditions, since there's no said since there physically on the net acceleration CEO on there for the right inside is zero here. From here we find ft, which comes out to the N G over twice off scientific data. Now, since the angle here is very small about seven degree, if you can call it, we can use the small angle approximation which say is that Tita is merely going to sign Tika and that doesn't really called. Oh dan tikka. So we make this substitution over here on dde down. Tita, if you calculate, comes out to be 2.1, which is the perpendicular distance over the base, he does half off the total int Now the blood this value off time down. Tita, this accretion are also the muscles on dhe acceleration due to gravity which are known from the problem. On doing that will find the tension force It's gone. So to be 2500 Newton. Now I distress on the fact that the angle here the approximation here can only be used when the angle is small enough. Now it is not possible to increase the tensions here. So they're so that there is no sag that must always the vertical component off the tension to balance the gravity falls. The horizontal component always cancels out because this is just 50 cause, Tita, in that towards the left and if the cost it again towards right. So they cancel out for the horizontal direction. But for the vertical direction, we must always have Ah, a compliment. Well, vertical component off f b so that the gravity force is on so balanced. And now the larger detention gets, the smaller the stag angle will be in order to balance empty.

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