Sunday, October 9, 2011
HW4 #5
Can somebody please help me with this question? I was able to answer the three preceding steps, but I seem to be stuck on this one. I attempted to calculate the horizontal components of T1 and T2 using trigonometry, but this yielded an incorrect solution. I then tried adding these values together, but this was wrong too. Please help!
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First let me go over the names so you will know what I'm talking about. T1 is tension in the angled string up-and-to-the-left. T3 is the tension in the angled string up-and-to-the-right. T2 is the tension in the horizontal string. There are 2 identical vertical strings too, and we can call their tensions both Tv. In #4 you figured out T3. #5 is asking for T2.
Look at the forces (tensions) acting on the knot at the right end of the horizontal string with T2. There is a vertical force Tv, a horizontal force pulling to the left T2, and an up-and-to-the-right force T3. If you put the forces in a table, Tv goes in the y column, T2 goes in the x column, and T3 goes in the "?" (idk) column.
In order to figure out the x- and y-components of T3, you will first have to figure out the angle that the string T3 makes with the ceiling. The length of the T3 string is your hypotenuse, and you need to look at the geometry of the strings to figure out the length of the x side, but that is enough information to find the angle from the ceiling (from the horizontal).
Now that you have the angle, you can put T3cosθ in the x column of your force chart and T3sinθ in the y column of your force chart.
Now that you have all your forces into either x- or y-components, you can use Newton's 2nd law to sum the forces acting in the horizontal direction. If you choose "right" as your positive direction you should get ∑F=T3cosθ-T2=ma=0, and it =0 because the knot isn't accelerating. Solve for T2.
Good luck.
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