10_P36InstructorSolution

10_P36InstructorSolution - 10.36. Model: For the ice cube...

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10.36. Model: For the ice cube sliding around the inside of a smooth pipe, the sum of the kinetic and gravitational potential energy does not change. Visualize: We use a coordinate system with the origin at the bottom of the pipe, that is, 1 0. y = The radius ( R ) of the pipe is 10 cm, and therefore top 2 20 . 2 0 m . yyR == = At an arbitrary angle , θ measured counterclockwise from the bottom of the circle, cos . yRR =− Solve: (a) The energy conservation equation 2g 21g 1 K UK U += + is 22 11 2 21 1 2 2 ( ) (3.0 m/s) 2(9.8 m/s )(0 m 0.20 m) 2.25 m/s mv mgy mv mgy vvg y y ⇒+ =+ ⇒= + − = + = (b) Expressing the energy conservation equation as a function of : () g1 g 1 1 0 J 2( ) 2 ( 1c o s ) K U K U mv mgy mv vv g yv g R θθ + + ⇒= = Using
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