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The uniform 100-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with theta = 0. Determine the initial angular acceleration of the beam and the magnitude of the force FA supported by the pin at A due to the application of the force P = 300 N on the attached cable.

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davidlcastiblanco

Answer:

ac = 2.86 m / s²

Explanation:

Image can detail the system to determine the force in the FA to understand the system into the applicated force

m = 100 kg ,  L = 3 m

∑ F = 0 ⇒ Ay - 100 kg + P * cos (45) = 0

Ay = 768.86 N

∑ Mₐ = α * I ₐ

I ₐ = m * L² / 3  ⇒  I ₐ = 100 kg * 4² m / 3

Replacing

P * sin (45) * 3 = α * 100 kg * 4² m / 3  

α = 1.193 rad / s²

ac = α *2    ⇒  ac = 1.193 rad / s²  * 2

ac = 2.86 m / s²

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