To help envision why the force on a cable increases as the angle of the cable increases imagine tying a rope to a bucket of water then lifting the bucket to the height of a door knob. The force (tension) on the rope and the force your muscles need to exert to lift the bucket are each equal to the weight of the bucket.<\/p>\n<\/div>\n

$\"Lifting$ <\/div>\n<\/div>\n

Adding angles<\/h4>\n
\n
Now imagine if you pass the same rope through the bucket handle and tie it to the door knob. Stand back holding the other end of the rope with the bucket between you and the doorknob. Keeping your hand at the level of the door knob\u00a0you could pull the rope and lift the bucket but it would take quite a bit of work to raise the bucket even a foot. Try raising the bucket so the handle is at the same height as the doorknob – you can’t<\/strong> do it!!<\/em> In fact, the force it takes to raise the bucket to that height spikes to infinity. It literally can not be done in our physical world.<\/p>\n<\/div>\n
$\"Lifting$ <\/div>\n<\/div>\n
\n
More math!<\/h4>\n
\n
The equation to find the force on two cables under load at a given angle is:
\nF<\/em> = (m<\/em> x 0.5) \u00f7 cos<\/em>(a<\/em> x 0.5)<\/strong><\/p>\n
where:
\nF<\/em> is the calculated force on each cable
\nm<\/em> is the mass or in our case the lift load
\na<\/em> is the internal angle between the two cables<\/p>\n<\/div>\n
\n
$\"The$ <\/p>\n<\/div>\n<\/div>\n
Our cables have an approximately 110\u02da internal angle. So we plug in our numbers and we get:<\/p>\n
The dividend:
\n(m<\/em> x 0.5) = (5,606 x .5) = 2,803<\/strong><\/p>\n
The divisor:
\ncos<\/em>(a<\/em> x 0.5) = cos<\/em>(110 x .5) = cos<\/em>(55) = .573576<\/strong><\/p>\n
Divide for quotient:
\n2,803 \u00f7 .573576 = 4,886.88 lbs<\/strong><\/p>\n
(hint: at 120\u02da the force shared on two cables is exactly double the mass of the load.)<\/em><\/p>\n
This math is for two cables, but we have three so we simply add the two together then divide by 3.
\n4,886.88 + 4,886.88 = 9,773.76 lbs
\n9,773.76 \u00f7 3 = 3,257.92 lbs<\/strong><\/p>\n
Conclusion<\/h4>\n
Each cable will have 3,257.92 pounds of force!<\/strong><\/em> That’s more than 1.5 tons EACH!<\/p>\n
High five Archimedes, thanks for being awesome.<\/p>\n
Interestingly if we increase our angle to 120\u02da the math comes out to 3,737 pounds on each cable (11,212 total). That 10\u02da increase added 1,438 pounds of force to our system! It’s amazing to think that 5,606 pounds of lift can have 11,212 pounds of force!<\/p>\n","protected":false},"excerpt":{"rendered":"
When I was a kid we made a lot of “forts”. I mean a lot of forts. Forts all – the – time. Of course as a kid a fort was as simple as a piece of wood leaned against a fence, a pile of broken up concrete from a sidewalk, an “igloo” of tumble<\/p>\n
Read More<\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[13],"tags":[15,19,16,17,18,14],"_links":{"self":[{"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/posts\/38"}],"collection":[{"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/comments?post=38"}],"version-history":[{"count":46,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/posts\/38\/revisions"}],"predecessor-version":[{"id":138,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/posts\/38\/revisions\/138"}],"wp:attachment":[{"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/media?parent=38"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/categories?post=38"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/railandoak.atwebpages.com\/wp-json\/wp\/v2\/tags?post=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}