A block of mass m=2kg can slide down a frictionless 53 degree incline but it is

Question

A block of mass m=2kg can slide down a frictionless 53 degree incline but it is connected to a pulley of mass M=4kg and radius R=0.5 m, as shown. The pulley can be treated as a disk. Find: (a) the angular acceleration of the pulley; (b) the speed of the block after it has slid 1 m, starting from rest.(HINT: use dynamics methond to solve)

Explanation / Answer

Tension in the rope = T Torque on the pulley = T*R T*R = I * a = ((M*R^2)/2) * a a=angular acceleration of pulley; I = moment of inertia of disc. T*R = I * a = ((M*R^2)/2) * a substituting values of R and M 0.5 T = 0.5 a => T = a for block : Net force along the slope = m*(acceleration of the block) m*g*cos37 - T = m*(a*R) substituting values of m ,g, R...and putting T=a as shown before we get 2*9.8*cos37 - a = 2*a*0.5 a) angular acceleration of the pulley = a=7.8266 rad/s2 b) acceleration of the block = a*R = 3.913 m/s2 v^2 - u^2= 2*a*s u=0 as it starts from rest s=1m => v^2 = 2*3.913*1 v=2.7976m/s Note that taking other values of g will giv a diff answer.

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