Fig. 1 shows a small drawbridge across a canal. The bridge is 4.0 m long and has a weight of 12 000 N acting at its centre. It pivots at the left-hand hinge...
Question 1 Report
Fig. 1 shows a small drawbridge across a canal. The bridge is 4.0 m long and has a weight of 12 000 N acting at its centre. It pivots at the left-hand hinge. A cable attached to the far end pulls upward. When the bridge is horizontal, the cable makes an angle such that its vertical component is 8000 N. A hydraulic system can also provide an upward force at 1.0 m from the hinge. The engineer uses moments to decide whether the bridge can be held safely.
The bridge's weight and the cable force are perpendicular to the bridge.
(a) Calculate the clockwise moment due to the bridge's weight. [2]
(b) Calculate the anticlockwise moment due to the cable. [2]
(c) Calculate the hydraulic force required for equilibrium. [3]
(d) Which direction will the bridge turn if the cable breaks while the hydraulic force remains unchanged? [1]
(e) What is the advantage of placing the hydraulic system farther from the hinge? [1]
(f) Sketch an arrow to show the bridge weight on Fig. 1. [1]
Answer Details
(a) The weight acts at the centre, \(2.0\text{ m}\) from the hinge:
\[12000\times2.0=24000\text{ N m}\]
The clockwise moment is 24 000 N m. [2]
(b) \[8000\times4.0=32000\text{ N m}\] The cable produces an anticlockwise moment of 32 000 N m. [2]
(c) The cable moment exceeds the weight moment by:
\[32000-24000=8000\text{ N m}\]
The hydraulic force must provide a clockwise moment:
\[F\times1.0=8000\]
\[F=8000\text{ N}\]
The required force is 8000 N downward. [3]
(d) If the cable breaks while the hydraulic force is unchanged, the bridge turns clockwise. [1]
(e) Placing the hydraulic system farther from the hinge means a smaller force can provide the same moment. [1]
(f) The weight arrow is vertically downward at the centre of the bridge. [1]
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