Fig. 1 shows a balanced sign outside a café. The sign has a weight of 180 N acting at its centre. It is supported by a horizontal bracket fixed to a wall. T...
Question 1 Report
Fig. 1 shows a balanced sign outside a café. The sign has a weight of 180 N acting at its centre. It is supported by a horizontal bracket fixed to a wall. The bracket has two bolts, A and B, separated by 0.20 m. The sign's centre is 0.60 m from the wall. Bolt A pulls outward and bolt B pushes into the wall, forming a couple that prevents the bracket turning. The weight is supported by a separate vertical fixing.
The horizontal forces at the bolts have equal size.
(a) Calculate the moment caused by the sign's weight about the wall. [2]
(b) Calculate the force at each bolt. [3]
(c) What is a couple? [1]
(d) Which bolt is in tension in this diagram? [1]
(e) Sketch arrows to show the pair of horizontal forces at A and B. [1]
Answer Details
(a) \[180\times0.60=108\text{ N m}\] The sign's weight produces a 108 N m moment about the wall. [2]
(b) The equal and opposite horizontal bolt forces form a couple:
\[F\times0.20=108\]
\[F=\frac{108}{0.20}=540\text{ N}\]
The force at each bolt is 540 N. [3]
(c) A couple is two equal, opposite and parallel forces separated by a distance. [1]
(d) Bolt A is in tension because it pulls outward from the wall. [1]
(e) The arrows must be horizontal, opposite, and at A and B. [1]
Download The App On Google Playstore
Everything you need to excel in your exams
