Question

Please help with problem 52

Rotational Motion Problem Solving "An expert is a person who has made all the mistakes that can be made in a very narrow field." -Niels Bohr 52. A thin hoop of mass M, radius R. and rotational inertia MR is released from lest from the top of the ramp of length L above. The ramp makes an angle () with respect to a horizontal tabletop to which the ramp is fixed. The table is a height // above the floor. Assume that the hoop rolls without slipping due to the friction forve / bulween the houp and the ramp. Express all answers in terms of given quantities ( M R, A, L, L, and H) and fundamental constants. MRQ a. Draw a frecbody diagram on the dot below of all the forces acting on the hoop at their point of origit. b. Using Newton's 2nd Law write a translational force equation that could be solved for lincar acceleration of the hoop down the ramp. u. Usitug Newlon's 2 down the ramp. Law for rotation write a rotational forces equation that could be solved for angular acceleration of the hoop d. Using the relationship between angular and linear acceleration, combine your equations in b and c above to derive an expression for the acceleration of the center of mass of the hoop as it rolls down the ramp. c. Derive an expression for the speed of the ocnter of mass of the hoop when it reaches the bottom of the ramp. [ and radius R. How will the speed of the disk at the Suppose that the hoop is now replaced by a solid disk having the sainc mass bottom of the ramp compare to the hoop determined in part (e)? Less than The same as Greater than Briefly justify your response. 18

Answer 1

UN H ingsing ng Cono ma = masinos ma = mg sino - ling caso a- glino - ugoslo. Ia = JR. m R? x = emg eas OR x = ugreso UR. a= &R. qisin o - ug cost. aug.com sino = 2ug caso. i A sino - Igsino. 64MP AI QUAD CAMERA Shot by Anand 20