A pulley has a mass M , a radius R , and is in the form of a uniform solid disk.

Question

A pulley has a mass M, a radius R, and is in the form of a uniform solid disk. The pulley can rotate without friction about a horizontal axis through its center. As shown in the diagram, the string wrapped around the outside edge of the pulley is subjected to an 8.00 N force in case 1, while in case 2 a block with a weight of 8.00 N hangs down from the string. Use g = 9.8 m/s2.

If M = 1.30 kg and R = 80.0 cm, calculate the magnitude of the angular acceleration of the pulley in

(a) case 1.
rad/s2

(b) case 2.
rad/s2

A pulley has a mass M, a radius R, and is in the form of a uniform solid disk. The pulley can rotate without friction about a horizontal axis through its center. As shown in the diagram, the string wrapped around the outside edge of the pulley is subjected to an 8.00 N force in case 1, while in case 2 a block with a weight of 8.00 N hangs down from the string. Use g = 9.8 m/s2. If M = 1.30 kg and R = 80.0 cm, calculate the magnitude of the angular acceleration of the pulley in (a) case 1. rad/s2 (b) case 2. rad/s2

Explanation / Answer

a) Case 1 : = R X F = 0.80 X 8 = 6.4

= I

6.4 = (1.3 X 0.802 /2) X

= 15.385 rad/s2

B ) case2 :

on block : 8 - T = (8/g)a

on pulley : R X T = I     ( = a/r)

         TR = (MR2 /2) X (a/R)

            T = 1.3a / 2

putting it in previous eqn ,

8 - 0.65a = 0.8163a

a = 8/1.4666 = 5.46 m/s2

= a/R = 5.46 / 0.80 = 6.82 rad/s2

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