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Discussion+01.07.2010+-+Examples - • Angle between F and...

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2/23/11 A B C F PT = 10 N Physical therapists often engage patients in muscle strengthening as part of rehabilitation. One exercise a physical therapist has asked his patient to do is shown in a simple diagram below. The patient’s physical disability is mainly on the left side, in that the left arm is shorter than the right and also significantly weaker. The patient locks her elbows at her side, and hold her right hand to the end of her left and is instructed to not let go during the exercise. The physical therapist gently exerts a force on this “endpoint.” We assume that the patients arms act as rigid bars. If the force is resolved into two components parallel with AB and AC, what are FAB and FAC? What’s the problem with this particular set up/exercise? x y 80⁰ 30⁰
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2/23/11 Solution FPT = 10N Calculate angles between AB and AC to vertical: Angle between F and AB: 90⁰-80⁰ = 10⁰
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Unformatted text preview: • Angle between F and AC: 90⁰-30⁰ = 60⁰ Using law of sines: • FAB = 10*sin(60)/sin(110) = 9.21 N • FAC = 10*sin(10)/sin(110) = 1.85 N F = 10 N FAB = 9.21 N FAC = 1.85 N 10⁰ 60⁰ 110 ⁰ 2/23/11 x y FO1 = 50 N FO2 = 37.5 N FO3 = 45 N FM FM 60⁰ 30⁰ 45⁰ 59.741⁰ α α If α = 20⁰, what must FM be greater than such that the UM team is winning? How does the FM necessary change with α? Why? What would be the angle to minimize force exerted? UM and Ohio State students are playing tug of war. Each player pulls on his/ her own rope that is connected in the middle. Four Ohio State players have positioned themselves as shown and are pulling with known forces. Two UM students have positioned themselves at angles equidistant from the center line and decide to pull with equal force. FO4 = 35 N...
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