University Physics with Modern Physics with Mastering Physics (11th Edition)

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8.75: First consider the motion after the collision. The combined object has mass = tot m 25.0 kg. Apply a F m = Σ to the object at the top of the circular loop, where the object has speed 3 v . R v m mg T 2 3 = + The minimum speed 3 v for the object not to fall out of the circle is given by setting 0 = T . This gives , 3 Rg v = where m. 3.50 = R Next, use conservation of energy with point 2 at the bottom of the loop and point 3 at the top of the loop. Take
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Unformatted text preview: = y at the point 2. Only gravity does work, so 3 3 2 2 U K U K + = + ( 29 R g m v m v m 2 tot 2 3 tot 2 1 2 2 tot 2 1 + = Use Rg v = 3 and solve for s m 13.1 5 : 2 2 = = gR v v Now apply conservation of momentum to the collision between the dart and the sphere. Let 1 v be the speed of the dart before the collision. ( 29 ( 29 ( 29 s m 1 . 13 kg . 25 kg 00 . 5 1 = v s m 5 . 65 1 = v...
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