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, 10.y=The radius (R) of the pipe is 10 cm, and therefore top220.20m.yyR== =At an arbitrary angle ,θmeasured counterclockwise from the bottom of the circle, cos .yRR=−Solve: (a)The energy conservation equation 2g21g1KUKU+=+is 2211221122 ()(3.0 m/s)2(9.8 m/s )(0 m0.20 m)2.25 m/smvmgymvmgyvvgyy⇒+=+⇒= +− =+−=(b)Expressing the energy conservation equation as a function of :()g1g110J2()2 (1cos)KUKUmvmgymvvvgyvgRθθ+⇒+⇒=−=−−Using
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