Can someonesolve this problem once through with varaibles and once through with

Question

Can someonesolve this problem once through with varaibles and once through with numbers please?

The figure snows an Atwood machine. Find me linear accelerations of blocks A and B, the angular acceleration of the wheel C, and the tension in each side of the cord if there is no slipping between the cord and the surface of the wheel. Let the mass 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 0.300 kg m^2, and the radius of the wheel be 0.120 m.

Explanation / Answer

According to the given problem,

Let us assume

M1 = Mass of block A = 4.0 kg
M2 = Mass of block B = 2.00 kg
I = moment of inertia of the wheel = 0.300 kg-m2
R = radius of the wheel = 0.120 m
g = acceleration by gravity = 9.8 m/s²

What need to be found:

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 = ?

Using the free body diagram construct equations:

M1*g - T1 = M1*a ----------(1)
T2 - M2*g = M2*a ----------(2)
(T1 - T2)*R = I* ------------(3)
= a / R ---------------------(4)

Now solve the above equation using the following values:

a = 0.73118 m/s2 --------add the 1 and 2--substitute in 3 to get
= 6.093 rad/s2 -------------substiute a in 4
T = 36.315 N ----------substiute a in 1
T = 21.0823 N ----------substiute a in 2

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