in a truck-loading station at a post office, a small .250 kgpackage is released

Question

in a truck-loading station at a post office, a small .250 kgpackage is released from rest at point A on a track that isone-quarter of a circle with radius 1.60 m. The size of thepackage is much less then 1.60m, so the package can be treated as aparticle. it slides down the track and reaches point B with speedof 4.50 m/s. from point B, it slides on a level surface a distanceof d=3.50 m to point C, where it comes to rest.
(a) what is the coefficient of kinetic friction on the horizontalsurface?
(b) how much work is done on the package by friction as it slidesdown the circular arc from A to B?

Explanation / Answer

          Giventhat the mass of the package is m = 0.250 kg           radiusof the circle is R = 1.60 m           Speedof the package at the point B is  v = 4.50 m/s           The distance travelled in the horizontal plane is d = 3.50 m -----------------------------------------------------------------------------------         From the workenergy theorem the work done by the frictional force                            W = (1/2)mv2                        mgd = (1/2)mv2                                  = (1/2)v2 / gd                                   =------------     From the work energytheorem                        K1 + U1 + Wfri = K2 + U2                                            Wfri= K2 + U2 - K1 - U1                                                    =0 + 0 - (1/2)mv2 - mgR                                                   = - (1/2)mv2 - mgR                                                   = ------------- J             

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