Fig. 1.1 shows a trapdoor of weight 120 N and width 0.80 m, hinged along one edge. A vertical rope attached to the opposite edge holds the trapdoor horizont...
Question 1 Report
Fig. 1.1 shows a trapdoor of weight 120 N and width 0.80 m, hinged along one edge. A vertical rope attached to the opposite edge holds the trapdoor horizontal. The weight acts at the centre of the trapdoor.
Calculate the tension T in the rope.
Answer Details
Taking moments about the hinge, the system is in equilibrium when the clockwise moment equals the anticlockwise moment.
The weight (120 N) acts at the centre of the trapdoor, 0.40 m from the hinge. The tension T acts at the opposite edge, 0.80 m from the hinge.
\[ 120 \times 0.40 = T \times 0.80 \]\[ 48 = 0.80T \]\[ T = \frac{48}{0.80} = 60 \text{ N} \]The tension in the rope is 60 N, which is half the weight. The rope acts at twice the distance from the hinge compared to the weight, so only half the force is needed.
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