Answer to Question #1558 in Mechanics | Relativity for Brooke

Question

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

Answer 1

Due to energy equation:
mv²/2 = mgh - F_fr*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 =