Comments on: A 27-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire.? http://www.bathroomsconce.com/a-27-kg-chandelier-hangs-from-a-ceiling-on-a-vertical-4-0-m-long-wire.html Enjoy our wide selection of bathroom lighting fixtures Thu, 09 Feb 2012 00:10:01 -0700 http://wordpress.org/?v=2.8.4 hourly 1 By: Mike http://www.bathroomsconce.com/a-27-kg-chandelier-hangs-from-a-ceiling-on-a-vertical-4-0-m-long-wire.html/comment-page-1#comment-18709 Mike Wed, 28 Jul 2010 00:01:18 +0000 http://www.bathroomsconce.com/a-27-kg-chandelier-hangs-from-a-ceiling-on-a-vertical-4-0-m-long-wire.html#comment-18709 a) Ok, so in order to solve this problem, we need to take a few steps. The first step is, because the components of a force are found by using trig functions, we need to know the angle of displacement. This is represented simply by the vertical length, 4m, and the horizontal displacement, .15m. Using these two values, tan^-1(.15/4)=theta, our angle (where tan^1( is the tangent inverse function). This equation yields 2.15 deg for theta, and now we can begin the next step. With this angle, we can calculate the values of some necessary quantities. The most obvious thing we need to know is the force of tension. Since we don't have it's value explicitly, we can use the x or y component, along with our angle, theta, and determine its value as such. We don't know the x-component, in fact it's what we're solving for, but we can figure out the y component because it's equal to the force of gravity on the chandelier via this equation: mg=Fty, where Fty is the force of tension in the y direction. Inputting values and solving, we find that the force in the y-direction is 264.6 N. Now that we have this quantity, we can solve for the total tension, Ty, and thusly determine the x-component, Tx, that we're searching for. Ft=Fty/cos(theta), and by this relationship we find, as expected, since the angle was so small, that the total Ft is only a tiny bit larger, 264.8 N. With this value we can turn to a similar equation, Ftx=Ftcos(90-theta), since we need the opposite angle to solve for the leftward x-component. The equation yields Ftx=9.9 N. b)The tension in the wire was determined in problem a), but is equal to the y-component of the tension force, given by mg, is related to the total force in this equation: Fty/cos(theta)=Ft, and has a value of 264.8 N a) Ok, so in order to solve this problem, we need to take a few steps.
The first step is, because the components of a force are found by using trig functions, we need to know the angle of displacement. This is represented simply by the vertical length, 4m, and the horizontal displacement, .15m. Using these two values, tan^-1(.15/4)=theta, our angle (where tan^1( is the tangent inverse function). This equation yields 2.15 deg for theta, and now we can begin the next step.
With this angle, we can calculate the values of some necessary quantities. The most obvious thing we need to know is the force of tension. Since we don’t have it’s value explicitly, we can use the x or y component, along with our angle, theta, and determine its value as such. We don’t know the x-component, in fact it’s what we’re solving for, but we can figure out the y component because it’s equal to the force of gravity on the chandelier via this equation: mg=Fty, where Fty is the force of tension in the y direction. Inputting values and solving, we find that the force in the y-direction is 264.6 N.
Now that we have this quantity, we can solve for the total tension, Ty, and thusly determine the x-component, Tx, that we’re searching for. Ft=Fty/cos(theta), and by this relationship we find, as expected, since the angle was so small, that the total Ft is only a tiny bit larger, 264.8 N. With this value we can turn to a similar equation, Ftx=Ftcos(90-theta), since we need the opposite angle to solve for the leftward x-component. The equation yields Ftx=9.9 N.

b)The tension in the wire was determined in problem a), but is equal to the y-component of the tension force, given by mg, is related to the total force in this equation: Fty/cos(theta)=Ft, and has a value of 264.8 N

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