Question

Q1 Problem 1 20 Points Problem 1. (20 points) A marble rolls around a frictionless, circular loop of radius 30 cm. At the bottom of the loop, the marble's speed is 4m/s. Model the marble as a point particle. (a) (4 points) Calculate the magnitude of the marble's centripetal acceleration and the angular speed of the marble at the bottom of the loop. (b) (6 points) By applying conservation of energy, determine the speed of the marble at the top of the loop. (c) (4 points) What are the magnitude of the centripetal acceleration and the angular speed of the marble at the top of the loop? (d) (6 points) What was the average angular acceleration of the marble as it moved from the bottom of the loop to the top? What torque was responsible for this angular acceleration? (You don't need to calculate it, just state which force(s) caused it.)

Answer 1

sol Circular Loop of Radius R = 30cm At the Bottom marble's Speed = 4m5! ç = = 16 = 53.3 m/s2 R 0.3 오 WR mg نرم w2 mg R ae W = ac R 53.3 こ 577.8 - 13.3 rad (b) į mo? en mer + mg (22) 2 nec 받고 ag&ar 16 2 e + 2x9.8*2x0.3 얕 16 -11.76 4.24 본 J 4.24 - Il २. | ms/ velocity at the top t = 2.1m mil © Angular Speed remains Constant W = 13.3 rad's 2 2 (2.1) R 2 14.7 mi 0.3 (d) Average Accelaration a =(a) +(@c) top Bottom 2 . a 34 ms 2 53.3 + 14,7 - 34 mi? We ях Know ITT rF sim 90 = ef centripetal tries to pull it inside But normal force tries to keep in Contact Resultant force is responsible for torque. force