Consider the system shown in the diagram. The pulley is a uniform cylinder with

Question

Consider the system shown in the diagram. The pulley is a uniform cylinder with mass m3 =1.0 kg and radius R = 10 cm, the other two masses are m1 = 4.0 kg and m2 = 3.0 kg, and ? = 36.9 degrees. Assume the rope is massless, there is no slipping of the rope on the pulley, and there is no friction between m1 and the incline.

(a) What is the acceleration of m1 and m2? What is the angular acceleration of the pulley?

(b) If m2 starts from rest 50 cm above the ground, how fast is it going when it hits the ground?

Explanation / Answer

let the acceleration be a, angular acceleration be k,

tensions be x and y.so,

m2g-x=m2a

y-m1gsin36.9=m1a

(x-y)=0.5*3.1*a

and k=a/r

solving we get a=0.6877 m/s^2

and angular acceleration=6l887 rad/s^2

b)v=(2*0.6877*0.5)^1/2

=0.83 m/s

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