The figure below (Figure 1) illustrates an Atwood\'s machine. Let the masses of

Question

The figure below (Figure 1) illustrates an Atwood's machine. Let the masses of blocks A and B be 4.00 kg and 2.00 kg , respectively, the moment of inertia of the wheel about its axis be 0.400 kgm2 and the radius of the wheel be 0.100 m .

Part A

Find the linear acceleration of block A if there is no slipping between the cord and the surface of the wheel.

Part B

Find the linear acceleration of block B if there is no slipping between the cord and the surface of the wheel.

Part C

Find the angular acceleration of the wheel C if there is no slipping between the cord and the surface of the wheel.

Part D

Find the tension in left side of the cord if there is no slipping between the cord and the surface of the wheel.

Part E

Find the tension in right side of the cord if there is no slipping between the cord and the surface of the wheel.

Explanation / Answer

Let:
M = mass of block A = 4 kg
M = mass of block B = 2 kg
I = moment of inertia of the wheel = 0.400 kgm²
R = radius of the wheel = 0.1 m
g = acceleration by gravity = 9.8 m/s²

a = linear acceleration = ?
= angular acceleration = ?
T = tension in the string on the side of A = ?
T = tension in the string on the side of B = ?

Construct your equations:

Let k = I/r² = .400/.1² = 40 kg

2) a = g*[(2M+k)/(k+M+m) -1] = 0.426 m/s²

3) = a/r = 4.26 rad/sec²

4) T1 = g*M*m*(2+k/m)/(k+M+m) = 37.5 N

5) T2 = g*M*m*(2+k/M)/(k+M+m) = 20.5 N

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