A crane is used to raise one end of a 15kN girder of length 10m off the ground. When the end of the girder is at rest 6m off the ground, the crane cable is perpendicular to the girder.

a) calculate the tension in the cable

b) Show that the support force on the girder from the ground has a horizontal component of 3.6N and a vertical component of 10.2kN.

I'm really stuck guys - any help would be greatly appreciated.

Thanks

A) The cable is supplying enough tension to balance out the torque from gravity pulling on the girder around the axis of rotation where the girder is in contact with the ground. So what's the torque pulling the girder back to the ground? You can calculate it by assuming the entire weight of the girder is pulling straight down at its center. The center of the girder is 3m off the ground (vertical distance), 5m from the end of the girder in contact with the ground (this is the hypotenuse of a 3-4-5 right triangle), so the horizontal distance from the beam center to the end is 4m. Thus the torque on the beam is 15 kN * 4m = 60 kN*m. Meanwhile, the torque applied by the cable is T * 10m (where T is the tension) in the opposite direction. We know the moment arm is exactly 10m (the length of the girder) because the problem stated outright that the cable is perpendicular to the length of the girder.

So since the torques have to be equal and opposite (so that the entire girder is static), we can say

T * 10m = 60 kN*m
T = 6 kN

B) You now know both the magnitude and direction of the force applied by the cable (along with the force applied by gravity). If you simply sum up the horizontal and vertical components of those known forces, you'll find that the remaining support forces from the ground are exactly as the problem states.