Calculating Forces on a Domestic Wind Turbine During Extension/Retraction

[shaneslv]

Homework Statement

Hi
I need help in calculating the forces on a domestic wind turbine that is retracted/extended by a hydraulic ram. It is very simular to the following photo:

I need to calculate the forces at the hinge and where the ram attaches. I have all the relevant dimensions and masses:

The turbine is 200kg and is on top of a 15m shaft. The shaft is 3000kg and is uniform so the center of gravity is 7.5m up in the centre. The hinge is 1m of the ground and the ram attaches 2m above the ground.

Diagram better explains it :

I would be very appreciative of any help.

Thanks,
Shane

Homework Equations

The Attempt at a Solution

 

[jbsteele]

First, you will need to calculate the weight of the wind turbine (Wt) and the shaft (Ws). You can do this by using the equation W = m*g, where m is the mass and g is the gravitational acceleration (9.8 m/s2). Wt = 200kg * 9.8m/s2 =1960N Ws = 3000kg * 9.8m/s2 = 29400N Next, you will need to calculate the center of gravity of the system. This can be done by using the equation: CG = Wt*h1 + Ws*h2 / (Wt+Ws) Where h1 is the height of the wind turbine and h2 is the height of the shaft. In this case, h1 is equal to 1m and h2 is equal to 7.5m. CG = (1960N * 1m + 29400N * 7.5m) / (1960N + 29400N) CG = 3.75m Now, you can calculate the force at the hinge. This can be done by using the equation: Fh = Wt + Ws*(h2-h1)/(h2-CG) Where Fh is the force at the hinge, h2 is the height of the shaft and CG is the center of gravity. Fh = 1960N + 29400N*(7.5m-1m)/(7.5m-3.75m) Fh = 17160N Finally, you can calculate the force at the ram. This can be done by using the equation: Fr = Wt + Ws*(h2-h1)/(h1-CG) Where Fr is the force at the ram, h1 is the height of the wind turbine and CG is the center of gravity. Fr = 1960N + 29400N*(7.5m-1m)/(1m-3.75m) Fr = 21420N