# Answer to Question #1558 in Mechanics | Relativity for Brooke

Question #1558

50 lb block is projected up a 30 incline with an initial velocity of 40 ft/sec. Knowing that the

coefficient of kinetic friction between the block and the incline is 0.2, determine (a) the maximum

distance x that the block will move up the incline. (b) the velocity of the block as it returns to its original

position

coefficient of kinetic friction between the block and the incline is 0.2, determine (a) the maximum

distance x that the block will move up the incline. (b) the velocity of the block as it returns to its original

position

Expert's answer

Due to energy equation:

mv

mv

x = mv

After returning to the initial point the work of friction force would be 2Ffr*x = 2*μmg cos(30) x, thus

mv

v

mv

^{2}/2 = mgh - F_{fr}*x;mv

^{2}/2 = mgx sin(30) - μ mg cos(30)x;x = mv

^{2}/(2mg(sin(30) - μ cos(30))) =v^{2}/(2g(sin(30) - μ cos(30))) = 12.192^{2}[m/s]/(9.88[m/s^{2}](1 - 0.2*radic3)) = 23.2 m.After returning to the initial point the work of friction force would be 2Ffr*x = 2*μmg cos(30) x, thus

mv

_{1}^{2}/2 = mv^{2}/2 - 2mg cos(30) x.v

_{1}^{2}= v^{2}- 4μg cos 30 x = 12.192^{2}- 4*0.2* 9.8 √3*23.2 =
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