phy 121
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Sketch a vector representing a 10 Newton force which acts vertically downward.
• Position an x-y coordinate plane so that the initial point of your vector is at the origin, and the angle of the vector as measured counterclockwise from the positive x axis is 250 degrees. This will require that you 'rotate' the x-y coordinate plane from its traditional horizontal-vertical orientation.
• What are the x and y components of the equilibrant of the force?
answer/question/discussion: ->->->->->->->->->->->-> :
If the angle from the positive x axis is 250 degrees, then the x and y components of the original vector are both negative, and their equilibrants will both be positive. This will put the angle formed by the x axis and the magnitude at 70 degrees. Since we know the magnitude is 10, the angle opposite that angle measures 90 degrees, the angle opposite the y component is 70 degrees, and the angle opposite the x component is 20 degrees, we can set up an equation to determine the length of the other two sides as follows: sin 20 = x/10 so .34 = x/10, or x component of equilibrant = 3.4. To get the y component of equilibrant we use sin 70 = y/10, or .94 = y/10, so y component of equilibrant = 9.4. We can check by using the Pythagorean Theorem: 3.4^2 + 9.4^2 = 11.56 + 88.36 = c^2, making c=9.996, which is about equal to the given magnitude of 10.
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15 min
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Very good. Let me know if you have any questions.