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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
Expert's answer
Due to energy equation:
mv2/2 = mgh - Ffr*x;
mv2/2 = mgx sin(30) - μ mg cos(30)x;
x = mv2/(2mg(sin(30) - μ cos(30))) =v2/(2g(sin(30) - μ cos(30))) = 12.1922[m/s]/(9.88[m/s2](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
mv12/2 = mv2/2 - 2mg cos(30) x.
v12 = v2 - 4μg cos 30 x = 12.1922 - 4*0.2* 9.8 √3*23.2 =

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