A crane is used to raise one end of a 15kn girder of length 10.0m off the ground. When the end of the girder is at rest 6.0m off the ground, the crane cable is perpendicular to the girder.
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.
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- Thread Starter
- 23-02-2016 22:49
- 24-02-2016 11:26
First we need a diagram. You will have a triangle where the girder is the hypotenuse of length 10m and the opposite it the height above the ground 6m. You can then find out the angle at which the girder is elevated above the ground by doing arcsin(6/10). To find the component of weight perpendicular to the pivot that is the point 5m from each end of the girder you do 15000Ncos(arcsin(6/10))=12000N. Now we know the girder is held in that position so the component of tension and component of weight about the pivot are balanced and we can resolve moments.. That is 12000N*5m=T(the tension perpendicular to the pivot)*10m the tension in the cable must therefore be (12000N*5m)/10m=6000N. The perpendicular component of tension is elevated through the same angle from the vertical as the girder is from the horizontal, that is the angle arcsin(6/10). So the horizontal component is 6000N*sin(arcsin(6/10))=3600N this acts as the same support force from the ground. The vertical component is 6000N*cos(arcsin(6/10))=4800N. This means the reaction from the ground is weight - tension= 15000N-4800N=10200N. Hence the horizontal and vertical components are 3.6kN and 10.2kN respectively.