A 3.00 kg stone is tied to a thin, light wire wrapped around the outer edge of t

Question

A 3.00 kg stone is tied to a thin, light wire wrapped around the outer edge of the uniform 8.00 kgcylindrical pulley shown in the figure below (Figure 1) . The inner diameter of the pulley is 50.0 cm , while the outer diameter is 1.00 m . The system is released from rest, and there is no friction at the axle of the pulley.

Find the acceleration of the stone. (Express your answer in meters per second squared to three significant figures.)

Find the tension in the wire.(Express your answer in newtons to three significant figures.)

Find the angular acceleration of the pulley. (Express your answer in radians per second squared to three significant figures.)

Explanation / Answer

I = M (R1^2 + R2^2)/2

I = (8 kg) (0.25^2 + 0.50^2) / 2 = 1.25 kg m^2

on stone,

3g - T = 3 a

on pulley,

R T = I (a/R)

T = (1.25/0.5^2) a

T = 5 a

putting in equation,

3 g = 3a + 5a

a =3.68 m/s^2 ...........Ans

T = 5 a = 18.4 N ........Ans

alpha = a / R =7.36 rad/s^2 .........Ans

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