R 0 choose the rotation axis to be out of the page at

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Unformatted text preview: L/4 L/2 1 Mg 3 2 T 2 = Mg 3 Mg y x Physics 211 Lecture 17, Slide 11 What if you choose a different axis? r ∑τ = 0 Choose the rotation axis to be out of the page at the left end of the beam: page The torque due to the string on the right about this axis is: 3L τ 2 = T2 4 T1 The torque due to the string on the left is zero τ1 = 0 Torque due to gravity: L τ g = − Mg 2 T2 M x cm L/4 L/2 Mg y x Physics 211 Lecture 17, Slide 12 You end up with the same answer! The sum of all torques must be 0: τ1 + τ 2 + τ g = 0 T2 = T2 3L L − Mg = 0 4 2 2 Mg 3 T1 T2 We already found that T 1 + T2 = Mg L/4 L/2 T1 = M x cm 1 Mg 3 2 T 2 = Mg 3 Mg y x Physics 211 Lecture 17, Slide 13 Approach to Statics: Summary Approach to Statics: Summary In general, we can use the two equations r ∑F = 0 r ∑τ = 0 to solve any statics problem. When choosing axes about which to calculate torque, we When can sometimes be clever and make the problem easier.... can Physics 211 Lecture 17, Slide 14 Hanging Lamp Again Hanging Lamp Again A lamp of mass m hangs from the end of plank of mass M and length L. One end of the plank is held to a wall by a hinge, and the other end is supported by a massless string that makes an angle θ with the plank. a) What is the tension in the string? b) What are the forces supplied by the hinge on the plank? M θ hinge L m Physics 211 Lecture 17, Slide 15 Physics 211 Lecture 17, Slide First use the fact that ∑ F = 0 in both x and y directions: x: T cos θ...
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