231_Physics ProblemsTechnical Physics

231_Physics ProblemsTechnical Physics - Chapter 8 P8.38 233...

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Chapter 8 233 P8.38 The total mechanical energy of the skysurfer-Earth system is EK U m v m g h g mech =+ = + 1 2 2 . Since the skysurfer has constant speed, dE dt mv dv dt mg dh dt mg v mgv mech =+= + = 0 af . The rate the system is losing mechanical energy is then dE dt mgv mech 2 kg m s m s kW == = 75 0 9 80 60 0 441 .. . . bg ej . *P8.39 (a) Let m be the mass of the whole board. The portion on the rough surface has mass mx L . The normal force supporting it is mxg L and the frictional force is µ k mgx L ma = . Then a gx L k = opposite to the motion. (b) In an incremental bit of forward motion dx , the kinetic energy converted into internal energy is fdx mgx L dx k k = . The whole energy converted is 1 22 2 2 0 2 0 mv mgx L dx mg L x mgL vg L k L k L k k === = z µµ Section 8.5 Relationship Between Conservative Forces and Potential Energy
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