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Instructions for an educational activity aimed at demonstrating the effect of cable geometry on cable tension and the trigonometric relationship between cable geometry and cable tension. Students will use a spring scale, tape measure, small diameter rope or cable, pulley, and known weight to measure cable tension in various scenarios. The activity also covers the concept of cable capacity, factor of safety, and the importance of not exceeding the elastic limit of the cable.
Typology: Summaries
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Learning from the Forest
Subject(s): Science/Math
Grade Level: 9 th^ – 12th
Activity Author : Dr. Leonard Johnson, Univ. of Idaho
Objectives : To demonstrate the effect of cable geometry on cable tension and to show the trigonometric relationship between cable geometry and cable tension. Materials Needed : Known weight, tape measure, small diameter rope or cable, pulley and spring scale.
Background : The most efficient way to lift and support a load is to lift if vertically. This might be possible in logging with a helicopter or balloon, but does not work with cable yarding systems. In these systems, the cable is fixed at both ends and suspended over the operating area and some of the lifting capacity of the cable is lost to forces acting in the horizontal, rather than the vertical direction. The lifting capacity of the cable, often called wire rope in logging, is a function of its size … primarily its diameter. Lifting capacity is directly proportional to the square of the diameter or the end area of the cable. Depending on the type of steel used to construct the cable and the strength of the material used in its middle section (core), cable of a given size will have a measured capacity of a certain number of pounds of breaking strength. A ¾ inch wire rope used as a skyline in logging, for example, would have a breaking strength of 58,800 pounds. You would not operate a cable up to its breaking strength, however. A wire rope acts like a spring that stretches under load and returns to its original shape when the load is released. Just like a spring that is overloaded, however, if the cable is loaded past what is called its elastic limit, it will not return to its original shape. This occurs at a load of about half of the breaking strength and will severely weaken the cable for future applications. Cables are usually operated with a factor of safety to prevent the cable from being stretched beyond its elastic limit and to guard against sudden dynamic loads that may occur in logging. With a factor of safety of 3, the effective safe working load of the inch cable would be 58,800/3 or 19,600 pounds. This would be the value used to plan the number of logs a cable could carry each logging cycle.
Procedure:
Learning from the Forest
The theoretical distribution of load in the cable can be calculated from the dimension of the triangle formed by the cable, and the floor. The amount of tension in each cable segment will be proportional to the length arm of the triangle as follows:
Length a Length b Length c ——— = ——— = ——— Tension a Tension b Tension c Where the triangle has the dimensions shown below:
Load Load ↑ ↑
c c b b
a 2.5 lbs a
a. How much of the load will be carried vertically by each end of the cable?
Horizontal Span
Deflection
Deflection % Deflection = 100% Horizontal Spar