A shop sign is suspended from a uniform pole fixed to a wall and supported by a

Question

A shop sign is suspended from a uniform pole fixed to a wall and supported by a cable. The mass of the

sign is 66 kg, and it's attached to the pole 2.1 m from the wall. The pole's mass is 18 kg and its length is

2.5 m. When the cable is anchored to a windowsill so that the angle between the pole and the cable is

? = 22

Explanation / Answer

sign=66 kg ==>?=22 degree ==>pole=18 kg ==>cable tension max=6000 N ==>t=0 2.5 m*4200 N*sin(?)-0.5*2.5 m*18 kg*9.8 m/s2-2.1 m*66 kg*9.8 m/s2=0 (eliminate the length of the pole) 1573.35 N-0.5*176.4 N-0.84*646.8 N=0 ==>1573.35-0.5*176.4-0.84*646.8˜941.838 N this means that the sign can weigh max 941.84 N or 96.11 kg =using the original cable tension of 4200 N (calculated max sign weight of 941.84 N/9.8˜96.11 kg the sign weighs 66 kg) The original model will work!!!

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