How do you solve the hanging cable problem?

Spread the love

What is the equation of a hanging cable?

Precisely, the curve in the xy-plane of such a chain suspended from equal heights at its ends and dropping at x = 0 to its lowest height y = a is given by the equation y = (a/2)(ex/a + e−x/a). It can also be expressed in terms of the hyperbolic cosine function as y = a cosh(x/a).

Is a hanging cable a parabola?

However, in his Two New Sciences (1638), Galileo wrote that a hanging cord is only an approximate parabola, correctly observing that this approximation improves in accuracy as the curvature gets smaller and is almost exact when the elevation is less than 45°.

What is the length between two poles if the hanging cable is 80 m long?

[y1(a,x)y2(a,x)]=[00]. [ y 1 ( a , x ) y 2 ( a , x ) ] = [ 0 0 ] . In other words, for a cable of length 80m the pole of a suspension bridge will be located 23.7m from the origo, which means the two poles of the bridge will be 47.3m apart, which is also the span of the bridge.

What is the length between the two poles if the hanging cable is 80m long poles are 50m tall and the distance between the hanging cable and the ground is 10m ?)?

The distance between the poles which is connected by cable of 80m long to two poles ,and 50 height each pole and distance between cable to surface is 10m is given as follows. Consider the attached figure, while going through the following steps. Hence the distance between the poles is 2 × 23 = 46m.

What is the distance between two poles?

Thus the distance between the poles is equal to 46 m.

How do you calculate hanging rope?

When the rope is taut and forms a straight line between the tops of the poles, then its length is equal to the sum of the heights of the two poles. Since the two poles are upright, we can also find that the distance between the poles are equal to 2sqrt(2) times the height of the shorter pole.

What is the formula for a catenary?

The catenary, i.e., the shape of a freely hanging chain suspended from two points, can be expressed in modern formulas by the equation y = (ex + e− x)/2. Leibniz discovered this relation, although he did not write it as an equation.

How do you calculate cable length?

What is catenary physics?

The catenary curve is the graph of the hyperbolic cosine function. The catenoid, the catenary curve’s surface of revolution, is a minimal surface of revolution. A hanging chain can take the form of a catenary, which has the lowest potential energy.

What is catenary effect?

Catenary action is a load mechanism that is developed to resist the additional loads as a result of sudden column loss and prevent disproportionate collapse. Buckling restrained braces (BRBs) have been widely adopted as a dependable lateral load mechanism since the early 1990s.

What is the purpose of catenary?

In our world, a catenary is a system of overhead wires used to supply electricity to a locomotive, streetcar, or light rail vehicle which is equipped with a pantograph. The pantagraph presses against the underside of the lowest overhead wire, the contact wire.

What is the distance from pole to pole?

However, from pole to pole — the meridional circumference — Earth is only 24,860 miles (40,008 km) around. Our planet’s shape, caused by the flattening at the poles, is called an oblate spheroid.

What is the distance between North Pole and South Pole?

It is the southernmost point on Earth and lies antipodally on the opposite side of Earth from the North Pole, at a distance of 12,430 miles (20,004 km) in all directions.

How do you measure the length of a sagging rope?

We use the formulas: y = a*cosh(x/a), T = (W/l)*y, and s = SquareRoot(y2 – a2).

What is the distance between the poles of previous example if the length of the cable is 80 m and the center of the cable is 20 above the ground?

This is Expert Verified Answer Answer: The distance between the poles is 46 m. Given data states the height of the two tower as 50 m and the cable length to be 80 m. the mid point of cable is 10 m above the ground denoted as h. Therefore the distance between the poles be 2x = 2 x 23 = 46 m.

What is the distance between two magnetic poles of a bar magnet called?

The shortest distance joining the magnetic poles of a magnet is known as magnetic length.

What is the distance between two electric pole in India?

They are typically spaced about 125 ft (38 m) apart in urban areas, or about 300 ft (91 m) in rural areas, but distances vary widely based on terrain. Joint-use poles are usually owned by one utility, which leases space on it for other cables.

What is the vertical distance between two consecutive contour?

Vertical distance between two contour is known Contour interval and horizontal distance between two contours is known Contour gradient.

What would have been the distance between the two ships if the ships were on either side of the lighthouse?

Thus, the distance between two ships is approximately 316 m. Q. From the top of a light house 100 m high, the angles of depression of two ships are observed as 48∘ and 36∘ respectively.

How is hanging drop calculated?

Haughton used the following formula, known as the “Standard Drop” method: length of drop in feet = 2240/weight of the body in pounds. Haughton noted that when this force was applied, the condemned was taller by 1.5 in following the hanging.

How do you find the tension of a hanging mass?

The tension on an object is equal to the mass of the object x gravitational force plus/minus the mass x acceleration.

How do I calculate tension?

  1. Tension formula is articulated as. T=mg+ma.
  2. Tension Formula is made use of to find the tension force acting on any object. It is useful for problems.
  3. Tension Solved Examples.
  4. Problem 1: A 8 Kg mass is dangling at the end of a string.
  5. Answer:

How is cable sag calculated?

The sag relative to a support equals cable weight per unit length times the distance to the low point squared divided by twice the horizontal tension. The tension at a support equals the overal tension plus the cable weight per unit length times the sag relative to a support.

What are catenary measurements?

The Catenary Geometry & Wear System is a non-contact measuring system using laser scanners and high-resolution digital cameras to measure height, residual thickness and stagger of up to 8 wires simultaneously at a top speed of 320 km/h.

Do NOT follow this link or you will be banned from the site!