681_Physics ProblemsTechnical Physics

681_Physics ProblemsTechnical Physics - Chapter 23 P23.56...

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Chapter 23 21 P23.56 This is the general version of the preceding problem. The known quantities are A , B , m , g , and θ . The unknowns are q and T . The approach to this problem should be the same as for the last problem, but without numbers to substitute for the variables. Likewise, we can use the free body diagram given in the solution to problem 55. Again, Newton’s second law: FT q A x =− + = sin 0 (1) and q B m g y =+ + = cos 0 (2) (a) Substituting T qA = sin , into Eq. (2), qA qB mg cos sin += . Isolating q on the left, q mg AB = + cot af . (b) Substituting this value into Eq. (1), T mgA = + cos sin θθ a f . If we had solved this general problem first, we would only need to substitute the appropriate values in the equations for q and T to find the numerical results needed for problem 55. If you find this problem more difficult than problem 55, the little list at the first step is useful. It shows what symbols to think of as known data, and what to consider
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