Calculate the Tension and Angular Acceleration in Log After Release

[Northbysouth]

Homework Statement

The uniform 69-lb log is supported by the two cables and used as a battering ram. If the log is released from rest in the position shown, calculate the initial tension induced in each cable immediately after release and the corresponding angular acceleration α of the cables.

Homework Equations

The Attempt at a Solution

I tried first by summing the forces in the x and y directions

ƩF_x: ma_x = T_Acos(θ) + T_Bcos(θ)

ƩF_y: ma_y = -mg + T_Asin(θ) + T_Bsin(θ)

I assumed that a_x and a_y are equal to 0 and then I took these two equations and tried to solve them by using the matrix function on my calculator, but it doesn't work.

I'm now trying to take the moment about the center of the beam

The distances I have used should be the perpendicular distances from the tensions

ƩM_G: = Iα = -T_A((d+e)/s)sin(θ) + T_B((d+e)/2 - d)sin(θ)

but I'm not sure how to calculate the inertia, or if I need to calculate it at all.

Any advice would be greatly appreciated.

 

[Northbysouth]

I've managed to figure it out using a normal and tangential coordinate system,