A 50 lb block is projected up a 30 degree incline from point with an initial vel

Question

A 50 lb block is projected up a 30 degree  incline from point with an initial velocity. Knowing that the coefficient of kinetic friction between the block and the incline is 0.2 and that the block has traveled a distance of 20 ft when it reaches the highest point, , determine (a) the initial velocity of the block when it is projected up at point A and (b) the velocity of the block as it returns to its original position after reaching the highest poin B.

A 50 lb block is projected up a 30 degree incline from point with an initial velocity. Knowing that the coefficient of kinetic friction between the block and the incline is 0.2 and that the block has traveled a distance of 20 ft when it reaches the highest point, , determine (a) the initial velocity of the block when it is projected up at point A and (b) the velocity of the block as it returns to its original position after reaching the highest poin B.

Explanation / Answer

frictional force= 0.2*N = 0.2*mg*cos30 = 8.66 lb ;

pulling force = mgsin30 = 25 lb ;

let initial velocity as V ;

total force acting og block =25+8.66 = 33.66 ;

0.5*m*V^2 =33.66*20 ;

mV^2 =1346.4 ;

V=29.41 ft/s ;

b) whern it returns to its initial position ;

net force acting on body = 25-8.66 =16.34 ;

work done by this force = change in K.E ;

16.344 * 20 = 0.5*m*v^2 ;

V=20.49 ft/s

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