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^{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 =

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

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