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:

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

## Comments

## Leave a comment