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

Question

A 3.00kg stone is tied to a thin, light wire wrapped around the outer edge of the uniform 10.0kg cylindrical pulley shown in the figure below (Figure 1) . The inner diameter of the pulley is 50.0cm , while the outer diameter is 1.00m . The system is released from rest, and there is no friction at the axle of the pulley.

Part A

Find the acceleration of the stone.

Part B

Find the tension in the wire.

Part C

Find the angular acceleration of the pulley.

A 3.00kg stone is tied to a thin, light wire wrapped around the outer edge of the uniform 10.0kg cylindrical pulley shown in the figure below. The inner diameter of the pulley is 50.0cm, while the outer diameter is 1.00m. The system is released from rest, and there is no friction at the axle of the pulley. Find the acceleration of the stone. Find the tension in the wire. Find the angular acceleration of the pulley.

Explanation / Answer

Moment of inertia of the pulley,

I= 0.5*m*(r1^2 + r2^2)

I = 0.5*10*(1^2+0.5^2) = 6.25 kg.m2

Writing the equation of motion for the stone,

mg - T = m*a -------- (1)

and for the pulley,

T = I*(a/r1) -------- (2)

Adding the two equations,

Mg = Ma + I*(a/r1)

So, 3*9.8 = 3*a + 6.25*(a/1^2)

So, a = 3.18 m/s2 <-------answer (acceleration)

b)

So, Tension, T = 6.25*3.18/1^2 = 19.9 N <--------answer

c)

angular accelration = a/r1 = 3.18/1^2 = 3.18 rad/s2 <----answer

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