A knight in armour on a horse leaves the castle. His squire has mistakenly lowered the drawbridge 20 degrees below the horizontal. The knight and his horse stop when their combined center of mass are 1 metre from the end of the bridge. The uniform bridge is 8 metres long and has a mass of 2000 kg. The lift cable is attached to the bridge 5 metres from the hinge on the castle end, and to a point on the castle wall that is 12 metres above the bridge. The combined mass of the knight, his horse and their armour is 1000kg.
Determine a) the tension on the cable, and b) the horizontal and vertical force components acting on the bridge at the hinge.
Solution A: The complexity of this problem is that you need to calculate an angle using trigomy.
From the figure attached in the document, we can find a way to calculate the triangle of ABC.
The length ...
Using the parameters of mass and displacement of a bridge cable, the tension of the cable, as well as the vertical and horizontal forces acting upon the bridge at the hinge are determined. In using trigonometry and the properties of vertical/horizontal forces, the answer is obtained.