A technician checks the support cable of a raised footbridge. Fig. 1 shows the bridge deck in balance about pivot P. A maintenance box has weight 900 N and ...
Question 1 Report
A technician checks the support cable of a raised footbridge. Fig. 1 shows the bridge deck in balance about pivot P. A maintenance box has weight 900 N and is 3.0 m from P. The cable provides an upward force at the far end of the deck, 9.0 m from P.
(a) Calculate the clockwise moment of the box about P. [2]
(b) Calculate the upward force supplied by the cable. [2]
Answer Details
(a) Moment is calculated using force multiplied by perpendicular distance from the pivot:
\[\text{clockwise moment}=900\,\text{N}\times3.0\,\text{m}=2700\,\text{N m}\]
The clockwise moment is 2700 N m. [2]
(b) Because the deck is in balance, clockwise and anticlockwise moments are equal. The cable must provide an anticlockwise moment of \(2700\,\text{N m}\).
\[F\times9.0=2700\]
\[F=\frac{2700}{9.0}=300\,\text{N}\]
The upward cable force is 300 N. [2]
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