Please help!


by decathlonist
Tags: None
decathlonist
#1
Apr1-03, 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
Attached Images
File Type: bmp diagram.bmp (8.7 KB, 62 views)
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
russ_watters
russ_watters is offline
#2
Apr1-03, 11:08 PM
Mentor
P: 22,006
[searches in vain for an attachment...]
HallsofIvy
HallsofIvy is offline
#3
Apr2-03, 06:24 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,894
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, F1 and F2 be the forces on the respective cables. Obviously F1+F2= 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.


Register to reply