h A round object (a ring) is released from rest at the location shown by i....

 

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h A round object (a ring) is released from rest at the location shown by i. The object then rolls down without sliding and is able to reach to the topmost point f of the circular part of the track. At point f, the object is still in contact with the track. The radius of the object r is negligible compared to the radius of the track R, (i.e., r < R). The mass of the object is m and its moment of inertia around an axis passing through its center is Icm = m. r². Let h denote the height of the initial point i as measured from the bottom of the circular track. (a) Let's first derive a formula for the total kinetic energy: If u is the speed of the center of the object, find its total kinetic energy in terms of m and U. Krot (b) Find the speed us of the center of the object when it is at point f. Uf (c) Find the magnitude of the acceleration of the center of the object when it is at point f. acm = (d) Find the magnitude of the normal force when the object is at point f. n = (e) The object can stay in contact with the track at point f if h is above a critical minimum value (h> hmin). Find the minimum possible value of h such that the object is still in contact with the track at point f. (Note: Parts (b), (c) and (d) must be solved with hhmin assumption.) hmin = h A round object (a ring) is released from rest at the location shown by i. The object then rolls down without sliding and is able to reach to the topmost point f of the circular part of the track. At point f, the object is still in contact with the track. The radius of the object r is negligible compared to the radius of the track R, (i.e., r < R). The mass of the object is m and its moment of inertia around an axis passing through its center is Icm = m. r². Let h denote the height of the initial point i as measured from the bottom of the circular track. (a) Let's first derive a formula for the total kinetic energy: If u is the speed of the center of the object, find its total kinetic energy in terms of m and U. Krot (b) Find the speed us of the center of the object when it is at point f. Uf (c) Find the magnitude of the acceleration of the center of the object when it is at point f. acm = (d) Find the magnitude of the normal force when the object is at point f. n = (e) The object can stay in contact with the track at point f if h is above a critical minimum value (h> hmin). Find the minimum possible value of h such that the object is still in contact with the track at point f. (Note: Parts (b), (c) and (d) must be solved with hhmin assumption.) hmin =