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cfitzU2
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1. Homework Statement
"Three situations involving a block with a weight of 20.0 N and a string are shown in the figure above. In case 1, there is only one string leading from the hook to the ceiling. In cases 2 and 3, the string passes through a hook on top of the block.
[What the picture shows]: For case 2, an angle of 30 degrees is given and for case 3, an angle of 90 degrees is given. In each, the angle given is the angle "above the hook". That is, when one thinks of the triangle formed by the two ropes and the point-mass, we are given the angle made by the meeting of the two ropes, "pointing" down towards the ground.
QUESTIONS:
(a) Rank these situations based on the tension in the string, from largest to smallest (e.g., 3>1=2).
(b) Calculate the tension in the string in case 3."2. Homework Equations
Fnet = T - mg
T = T1 + T23. The Attempt at a Solution
The most questionable assumption made is that the angles made with respect to the horizontal are equal. For instance, in case 2 the angle of 30 degrees is bisected so that we can deduce that the angle wrt the horizontal is 90 - 15 = 75. LIkewise with case 3 we are left with 45. It seems we have too little information to deduce the horizontal angles for an arbitrary (not necessarily equal) T1 and T2, so we've assumed that the bisection goes through as described.
IF that's ok, then part (b) of the question should be simple. Considering a 45 degree angle wrt the horizontal (by bisecting 90 degrees), the equality of T1 and T2 implies that T = T1 + T2 = 2*T1 = 2*(10*sin(45))=20*sqrt(2) which is approximately 28.28427, which, to three significant digits should be 28.3.
HOWEVER, the online submission system says this is wrong. As well as our answer to (a), for which we said that (case 1) < (case 2) < (case 3).
So, MY QUESTION, is: Is the approach described the correct one? I've seen tension problems before, but usually have been given two angles to work with, not just the one center angle between the ropes.
"Three situations involving a block with a weight of 20.0 N and a string are shown in the figure above. In case 1, there is only one string leading from the hook to the ceiling. In cases 2 and 3, the string passes through a hook on top of the block.
[What the picture shows]: For case 2, an angle of 30 degrees is given and for case 3, an angle of 90 degrees is given. In each, the angle given is the angle "above the hook". That is, when one thinks of the triangle formed by the two ropes and the point-mass, we are given the angle made by the meeting of the two ropes, "pointing" down towards the ground.
QUESTIONS:
(a) Rank these situations based on the tension in the string, from largest to smallest (e.g., 3>1=2).
(b) Calculate the tension in the string in case 3."2. Homework Equations
Fnet = T - mg
T = T1 + T23. The Attempt at a Solution
The most questionable assumption made is that the angles made with respect to the horizontal are equal. For instance, in case 2 the angle of 30 degrees is bisected so that we can deduce that the angle wrt the horizontal is 90 - 15 = 75. LIkewise with case 3 we are left with 45. It seems we have too little information to deduce the horizontal angles for an arbitrary (not necessarily equal) T1 and T2, so we've assumed that the bisection goes through as described.
IF that's ok, then part (b) of the question should be simple. Considering a 45 degree angle wrt the horizontal (by bisecting 90 degrees), the equality of T1 and T2 implies that T = T1 + T2 = 2*T1 = 2*(10*sin(45))=20*sqrt(2) which is approximately 28.28427, which, to three significant digits should be 28.3.
HOWEVER, the online submission system says this is wrong. As well as our answer to (a), for which we said that (case 1) < (case 2) < (case 3).
So, MY QUESTION, is: Is the approach described the correct one? I've seen tension problems before, but usually have been given two angles to work with, not just the one center angle between the ropes.
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