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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 Newtons second law: summationdisplay F n = ma n : T- mg cos = mL 2 summationdisplay F t = ma t :- mg sin = mL Either integrate the second equation, using = d d d dt = d d : integraldisplay 1 mL d = integraldisplay 1 - mg sin d = mL 2 1 2 = mg cos vextendsingle vextendsingle vextendsingle vextendsingle 1 or use conservation of energy to obtain at various values of . Finally use the equation from F n = ma n to find the tension at 1 and 2 . 2. Problem 1.5. Fixed axis rotation about the hinge axis. Draw FBD of door; apply M hinge = I hinge . Let , and 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