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Unformatted text preview: Solutions: Homework Set 1 1. Problem 1.3. Draw free-body diagram (FBD) of mass m . Forces on m include the weight mg and the string tension T . Orient coordinates so that one axis is tangent to the path of m and the other is normal to it (along the string, radially inward), and apply Newton’s second law: summationdisplay F n = ma n : T- mg cos θ = mL ˙ θ 2 summationdisplay F t = ma t :- mg sin θ = mL ¨ θ Either integrate the second equation, using ¨ θ = d ˙ θ dθ dθ dt = ˙ θ d ˙ θ dθ : integraldisplay ˙ θ 1 mL ˙ θ d ˙ θ = integraldisplay θ 1 θ- mg sin θ dθ = ⇒ mL ˙ θ 2 1 2 = mg cos θ vextendsingle vextendsingle vextendsingle vextendsingle θ 1 θ or use conservation of energy to obtain ˙ θ at various values of θ . Finally use the equation from ∑ F n = ma n to find the tension at θ 1 and θ 2 . 2. Problem 1.5. Fixed axis rotation about the hinge axis. Draw FBD of door; apply ∑ M hinge = I hinge ¨ θ . Let ˆ ı , ˆ and ˆ k be unit vectors directed along the bottom edge of the door, along the hinge axis, and out of the plane of the door, respectively, when...
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- Spring '10
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