Problem. 2: (2.5 points) A solld sphere of mass m and radius r starts from rest and rolls without slipping down a track

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Problem 2 2 5 Points A Solld Sphere Of Mass M And Radius R Starts From Rest And Rolls Without Slipping Down A Track 1 (86.99 KiB) Viewed 34 times

Problem. 2: (2.5 points) A solld sphere of mass m and radius r starts from rest and rolls without slipping down a track under the effect of the force of gravity. Points A and B are on a circular part of the track having radius R. The diameter of the solid sphere is very small compared to hand R, and the work done by rolling friction is negligible. (a) What is the minimum heighth for which this sphere will make a complete loop on the circular part of the track ? (b) How hard does the track push on the sphere at point B, which is at the same level as the center of the circle? (c) Suppose that the track had no friction and the sphere was released from the same height h you found in part (a). Demonstrate that the sphere will still make a complete loop. (d) In part (c), how hard does the track push on the solid sphere at point A, the top of the circle? How hard did it push on the sphere in part (a)? (e) If we replace the solid sphere with a hollow shell and place it at minimum height h found in in part a); will the shell still make complete loop? Why? A h ☺ PS: The sphere rolls along the track so it has both translational and rotational kinetic energy. Use free body diagrams, define you axes and stick to them, write the laws you use, make sure to write mathematical proofs, detailed answers and demonstrate your understanding and reasoning.