Fig. 1 shows a uniform metal beam being lifted by two cables at a theatre. The beam has a weight of 800 N acting at its centre. Cable A is attached 1.0 m to...
Question 1 Report
Fig. 1 shows a uniform metal beam being lifted by two cables at a theatre. The beam has a weight of 800 N acting at its centre. Cable A is attached 1.0 m to the left of the centre and cable B is attached 2.0 m to the right of the centre. The stage manager needs the beam to remain horizontal while a light is fitted. The upward forces in the cables produce moments about the beam's centre.
The beam is in equilibrium.
(a) What is the total upward force supplied by cables A and B? [1]
(b) Calculate the force in cable A. [3]
(c) Calculate the force in cable B. [2]
Answer Details
For equilibrium, upward force equals downward force and clockwise moments equal anticlockwise moments.
(a) The total upward force is 800 N, balancing the beam's weight. [1]
(b) Take moments about cable B. Cable A is \(3.0\text{ m}\) from B and the weight is \(2.0\text{ m}\) from B:
\[F_A\times3.0=800\times2.0\]
\[F_A=\frac{1600}{3.0}=533\text{ N}\]
Force in A is 533 N (about 530 N). [3]
(c) \[F_B=800-533=267\text{ N}\] Force in B is 267 N (about 270 N). [2]
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