The acceleration Block A is derived as a= 11.983ft/s². See explanation below.
Recall that we are given the following:
Radium = 20 inches
Weight = 330lbs
Radius of gyration = 15in
Mass of Block = 110lb
The formula for Moment of Inertia is also given as:
I = mk²
= 330 [ 15/12]²
I = 515.625 lb/ft²
To derive the moment about O, we recourse to
∈M₀ = I∝
TR = I∝
T [20/12] = 515.625 ∝
T = 309.375∝
Next, to derive the weight of the block A hanging freely,
Wa = MAg
= 110 x 32.2
= 3542 lbf
Acceleration is derived by
A = r∝
= [20/12] ∝
a = 1.667 ∝.........Lets call this equation 1
Value of the acceleration derived by Dalembert Principle
∈Fy = mAa
Wa-T = mAa
3542 - 309.375∝ = 110 x 1.667∝
3542 = 492.745∝
∝ = 7.8188 Rad/s²............Lets call this equation 2
Substituting the value of ∝ in equation 1, we have
a = 1.667∝
= 1.667 x 7.1883
a = 11.983 ft/s²
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