Let the masses of blocks A and B be 4.00 kg and 2.00 kg , respectively, the mome

Question

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 0.300 kg?m2, and the radius of the wheel be 0.130 m .

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

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

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

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

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

mA = 4 kg

mB = 2 kg

r = 0.13 m

I = 0.3 kg m^2

mA g - TA = mA a

- mB g + TB = mB a

Solving both equations

TA = mA ( g - a ) =

TB = mB ( g + a )

r(TA - TB) = r mA (g - a) - r mB(g + a) = I ?

a = ? r = g (mA - mB)/((mA + mB) + I/r2)

a = 9.81 x ( 4 - 2 ) / ( 4 + 2 + (0.3 /0.13^2) ) = 0.826 m/s^2

TA = mA ( g - a ) = 4 x (9.81 - 0.862) = 35.792 N

TB = mB ( g + a ) = 4 x (9.81 + 0.862) = 42.688 N

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(a) magnitude of linear acceleration of block A = 0.826 m/s^2

(b) magnitude of linear acceleration of block B = 0.826 m/s^2

(c) magnitude of linear acceleration of block C = 0.826 m/s^2

(d) tension in left side of the cord = TB = 42.688 N

(e) tension in left side of the cord = TA = 35.792 N

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