Please help!by decathlonist Tags: None 
#1
Apr103, 11:02 PM

P: n/a

I am stuck on one of the AP Physics problems. Could you please help me out and give some pointers on how to solve the following problem:
A hemispherical sign 1 m in diameter and of uniform mass density is supported by two strings. What fraction of the sign's weight is supported by each string? [see attachment for the diagram] Thank you 



#2
Apr103, 11:08 PM

Mentor
P: 22,000

[searches in vain for an attachment...]




#3
Apr203, 06:24 AM

Math
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Sci Advisor
Thanks
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P: 38,882

I was able to down load the attachement without any trouble.
I shows a semicircle with two lines (the supporting cables) going up from (first cable) one end of a diameter and (2nd cable) 0.75 meters along (I assume) the diameter and so 0.25 meters from the other end. Let W be the weight of the sign, F_{1} and F_{2} be the forces on the respective cables. Obviously F_{1}+F_{2}= W. The total torque must be 0 (about any point in particular about the point of attachment of cable 1) so W(1/2 meter) (the torque due to the weight of the sign)plus F_2(0.75) must be 0. (0.75)F_2 0.5 W= 0 or F_2= (0.5/0.75)W= (2/3)W. From F_1+ F_2= W we get F_1+ (2/3)W= W or F_1= (1/3)W. The cable at the back is supporting 1/3 of the weight and the one in front is supporting 2/3 of the weight. 


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