Physics 1 Problem Solutions 75

Physics 1 Problem Solutions 75 - Chapt 6 Newtons Laws and...

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Chapt. 6 Newton’s Laws and Dynamics II 71 coordinate θ is mR d 2 θ dt 2 = F net where is F net is the net force ALONG the path of the loop for any θ . (Note F net is the net force along the path in the rotating frame, and so contains real force and inertial force terms.) Write out F net explicitly in terms of m , g , θ , ω loop , and R (not r ). HINT: You will have take components of the gravity and centrifugal forces along the loop. Get the signs right. For mental clarity in determining the components, consider θ in the 1st quadrant (i.e., in the range (0 , 90 ). The expressions are for a general angle when you think about, but the 1st quadrant is isn’t to comprehend. Draw a diagram with the geometry qualitatively correct. d) From the results of the part (c) answer solve for four angles θ where d 2 θ dt 2 = 0 : i.e., where the angular acceleration of the bead on the loop is zero. These are equilibria or equilibrium points: i.e., points where the net force along the loop is zero. HINT: Watch out for divisions by zero: you could miss solutions that way. Also note that inverse cosine
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