A block of mass 0.500 kg is pushedagainst a horizontal spring of negligible mass

Question

A block of mass 0.500 kg is pushedagainst a horizontal spring of negligible mass until the spring iscompressed a distance x. The force constant of the springis 450 N/m. When it is released, the block travels along africtionless, horizontal surface to point B, the bottom ofa vertical circular track of radius R = 1.00 m, andcontinues to move up the track. The speed of the block at thebottom of the track is vB = 12.8 m/s, and the block experiences an averagefrictional force of 7.00 N while sliding up the track. (a) What is x?
(b) What speed do you predict for the block at the top of thetrack?
c) Does the block actually reach the top of the track, or doesit fall off before reaching the top?

Explanation / Answer

           Since the track is frictional less then from consercation ofenergy                            (1/2)Kx2 = (1/2)mVb2                                      x = ( mVb2 / K)1/2                                            = ----------- m       From work energy theorem andconsercation of energy                     (1/2)mVt2 + mg(2R) =(1/2)mVb2 - f (R)                            Then wea getVt = ---------- m/s where frictional force is f = 7.00 N andradius R = 1.00m The block falls only if  ac < g                                 where ac = Vt2 / R                                      x = ( mVb2 / K)1/2                                            = ----------- m       From work energy theorem andconsercation of energy                     (1/2)mVt2 + mg(2R) =(1/2)mVb2 - f (R)                            Then wea getVt = ---------- m/s where frictional force is f = 7.00 N andradius R = 1.00m The block falls only if  ac < g                                 where ac = Vt2 / R

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